[Question]
  [
Here is an image:
```
%%%%%%%%%%%%%
% Hello,    %
%    world! %
%%%%%%%%%%%%%
```
But it is too confusing for our undersized brains to compute. So we average it like this:
1. Split it into 2 x 2 sections. If the picture ends before a section is complete, imagine that there are spaces there.
2. Average the values of the ASCII characters in each section.
3. Round this average and convert it to an ASCII character.
4. Finally, replace all characters in the section to the average character.
Repeat this for all sections.
So the average of the image above looks like this:
```
$$>>II99######
$$>>II99######
$$##88KKGG####
$$##88KKGG####
```
**Your task: Write a program that takes an ASCII image as input and outputs its average.**
*Note Integers are rounded by function `floor(x+0.5)` or similar function - in other words, round halves upwards.*
  
[Answer]
# JavaScript (ES6), 159 bytes
```
document.write("<pre>"+(
// --- Solution ---
s=>s.replace(/./g,(c,i)=>(a=String.fromCharCode([t=0,1,l=s.search`
`+1,l+1].map(o=>t+=(n=s.charCodeAt(p=i+o-i%l%2-(i/l|0)%2*l))>32?n:32)|t/4+.5))+(++p%l?"":a))
// ----------------
)(`%%%%%%%%%%%%%
% Hello,    %
%    world! %
%%%%%%%%%%%%%`))
```
Takes a multiline string as input.
[Answer]
# [MATL](https://esolangs.org/wiki/MATL), ~~32~~ 30 bytes
```
2thZCO32XEoYmYocGZy2/Xke2t3$Y"
```
Input is a 2D char array, with rows separated by `;`.
[**Try it online!**](http://matl.tryitonline.net/#code=MnRoWkNPMzJYRW9ZbVlvY0daeTIvWGtlMnQzJFki&input=WyclJSUlJSUlJSUlJSUlJzsnJSBIZWxsbywgICAgJSc7JyUgICAgd29ybGQhICUnOyclJSUlJSUlJSUlJSUlJ10)
### Explanation
```
2th     % push array [2 2]
ZC      % take input implicitly. Arrange distinct 2x2 blocks as columns, padding with 0
O32XE   % replace 0 by 32 (space)
oYm     % convert to number. Take mean of each column
Yoc     % round. Convert to char
GZy     % size of input in the 2 dimensions
2/Xk    % divide each dimension by 2, and round up to account for the padding
e       % reshape into image with half original size in each dimension
2t3$Y"  % replicate by a factor of 2 in each dimension. Display implicitly
```
[Answer]
# Pyth, 58 bytes
```
J2A,lQlhQV:0GJ
Ksm*C+csmsm?&<kG<bHC@@Qkb32hBdhBN4 .5J:0HJK
```
[Try it online!](https://pyth.herokuapp.com/?code=J2A%2ClQlhQV%3A0GJ%0AKsm*C%2Bcsmsm%3F%26%3CkG%3CbHC%40%40Qkb32hBdhBN4+.5J%3A0HJK&input=%5B%22%25%25%25%25%25%25%25%25%25%25%25%25%25%22%2C+%22%25+Hello%2C++++%25%22%2C+%22%25++++world!+%25%22%2C+%22%25%25%25%25%25%25%25%25%25%25%25%25%25%22%5D&debug=0)
[Answer]
# Lua, ~~382~~ ~~376~~ ~~367~~ ~~353~~ 348 bytes
```
r="\n"o=... n=o:find(r)-1
l=n+n%2
a=o:gsub(r,(n~=l and" "or"")..r).." "..(#o//(l+1)%2<1 and r..(" "):rep(l)or"")print(a:gsub("()([^\n])(.)",function(p,m,c)t=p//(l+1)%2==0return string.char(math.floor((m:byte()+c:byte()+(t and a:sub(p+l+1,p+l+1)or a:sub(p-l,p-l)):byte()+(t and a:sub(p+l+2,p+l+2)or a:sub(p-l-1,p-l-1)):byte())/4+.5)):rep(2)end).."")
```
Works on the command line; accepts a string like the test case.
[Answer]
# Ruby, ~~235~~ 230 bytes
```
->i{i=i.split($/).map{|s|s.bytes+[s.size%2>0?32:0]}
w=i[0].size;h=i.size;h+=h%2;r=[[]]*h
(h/2).times{|y|y*=2
(w/2).times{|x|x*=2
c=((i[y][x,2]+(i[y+1]||[32]*w)[x,2]).inject(:+)/4.0).round.chr
r[y+1]=r[y]+=[c,c]}}
r.map(&:join)*$/}
```
[Answer]
# Python, 319 bytes
```
def f(A):
 L,R,S=len,range,A.split('\n')
 if L(S[0])%2:S=[s+' 'for s in S]
 m=L(S[0])
 if L(S)%2:S+=[' '*m]
 C=[chr(int(sum(map(ord,[S[i][j],S[i+1][j],S[i][j+1],S[i+1][j+1]]))/4.0+0.5))for i in R(0,L(S),2)for j in R(0,m,2)]
 f=t='';i=0
 while i<L(C):
    t+=C[i]*2
    i+=1
    if i%(m/2)<1:f+=(t+'\n')*2;t=''
 f=f[:-1]
 print f
```
2nd indentation is tabs.
Stuff before `C` is padding, `C` is the averaging process to single letters and rest is output
[Answer]
## R, ~~433~~ 399 bytes
```
y=scan(,'',sep="\n")
h=nchar(y[1])
v=length(y)
p=function(x)paste(x,collapse="")
if(h%%2){y=sapply(y,function(x)paste0(x," "));h=h+1}
if(v%%2){y=c(y,p(rep(" ",h)));v=v+1}
z=matrix(unlist(lapply(y,function(x)strtoi(charToRaw(x),16))),ncol=h,byrow=T)
a=array(,c(v,h))
for(i in 1:(v/2)){for(j in 1:(h/2)){r=2*i-1:0;s=2*j-1:0;a[r,s]=rawToChar(as.raw(floor(mean(z[r,s])+.5)))}}
cat(apply(a,1,p),sep="\n")
```
I am getting desperate because this thing seems to be non-competing as heck. It prints
```
$$>>II99######
$$>>II99######
$$##88KKGG####
$$##88KKGG####
```
for the test case.
If you feed in the 7×3
```
%%%%%%%
Example
%%%%%%%
```
the output will be
```
BBFFJJ33
BBFFJJ33
######!!
######!!
```
because of the divisibility by 2 etc. etc.
Ungolfed:
```
y <- scan(, '', sep="\n") # Read STDIN and make it a character vector
h <- nchar(y[1]) # Get line width: how many chars per line
v <- length(y)   # Get array height: how many lines
p <- function(x) paste(x, collapse="") # A function that merges a vector of strings
if (h%%2) {y <- sapply(y, function(x) paste0(x, " ")); h=h+1} # If height is odd, add an empty line
if (v%%2) {y <- c(y, p(rep(" ", h))); v=v+1} # If width is odd, add an empty column
z <- matrix(unlist(lapply(y, function(x) strtoi(charToRaw(x), 16))), ncol=h, byrow=T)
# z now stores ASCII codes in a matrix; analogous to C strtol
a <- array(, dim=c(v,h)) # Reserve an array for the final result
for (i in 1:(v/2)) {
  for(j in 1:(h/2)) {
    r <- 2*i - 1:0 # Range of rows to average
    s <- 2*j - 1:0 # Range of columns to average
    a[r, s] <- rawToChar(as.raw(floor(mean(z[r, s]) + .5))) # Average, round, convert the ASCII codes
  } # and write them to the same place as in the original array
}
cat(apply(a, 1 , p), sep="\n") # Prints the array row-wise (index 1 for rows)
```
Just look how it handles this one gorgeous example (courtesy of chris.com):
```
                                                M$$$$$$$$$$$$$$$$RMMMMM8MMX    
                                               <$$$$$$$$$$$$R????!!?MMMR$RMMh. 
                                              :M$$$$$$$R?!!~~~~!!!!!!!MMM$$$$X 
                                             :M$$$$$$$X!~~~   ~~~~~!!MM8$MM$$M!
                                           :!XM$$$$$$R!~~~~~  ~~~~~!!M$$$$$$$R!
                                          <!XM$$$$$$MR!~~~~ ~~ ~:!!<:!M$$$$$$$!
                                         '<!XMBQQRMMMMX:::~~~<!?!!~~!!!!$$$M!$X
                                         ~!!MM$$$$$M8R!!!?!:~!!M$f?!~~~!M$8HXX?
                                       <!!!XMM$$$$$MMRM$$!~!~~~~~~~~~~~!XM?!!M!
                                      <!!!!XMM$$M$$MM$M!!~~~ ~~~ ~  :~!!!X!~~R!
                                      !!!!XMMM$MMMMMMMM!!~~~ ~~~~  ~~~!!!X~~X!~
                                      '~~!!MMMM@MMMX!!MM!:~!!!~~  `~~~~!!XXXX~ 
                                        ~!!!XMMMMMMMM!MMM!~~~~:: <<~~~~!!$$R!  
                                        '!!!!MM888M$MXMMM!!!!()!!~~~~~<!X$$$>  
                                         ~!!!M???M$MRRMM$X<~!!!!~~~~~:!XN$$M   
                                          ~!!!!!M$$$$@$@$$!!~~'  ~~:XH8$$$WR   
                                          !!!!MM$RM$RRMMMM?t!:::XX8$$$$$$$$>   
                                         ~~!!MMM$$$$$WX!!!!!!$$$$$$$RR$$$R"    
                                       '  <!!MT!!!~~~!#BX!!!~~?T#?!!!M$$$X.    
                                         <!!!!~~~~~~~~~?$!!!~~~~~~:!M$$$$MXH:  
                                         ~~~~~~~~~~~ ~~!M&!!!~~~<!!X$$$$$$$R$W>
                                        <~~~~~~~~    '~~!$!!!!!!!!MMRM$R?#!!$N!
                                       x~~~~~~~~~    ~~~!MX!!!!!!?!M!M!~~:!!$B!
                                      M!~~~~~~~~~~  <~~:!$R!!!!!!!X!!!~~!!~!RR!
                                    :M!~~~~~~~~~~~ `~~~!X$R!!!!!!!!~~~:!!~~tMM!
                                   dR!!~~~~~~~~~~~~~~~~!M$R!!!!!!!~!!!!!!~~@$@~
                                  tR!!!~~~~~~~~~~~~~~~!!M$R!!!!!!!!!!!!!~~!$$E~
                                 d!~~~~~~~~~~~~~~~~~~~!!$$X!!!!!!!!!!!!~~~X$$!~
                                8R~~~~~~~~~~~~~~~~~~~<!X$$!!!!!!!!!!!<~~~!MR$~~
                               8$~~~~~~~!~~~~~~~~~~~<!!$$R!!!MX!!!!~~~~~<XR$!~<
                             :$$!~~~~~~!!~~~~~~~~~~~!!M$$!!!!MM!!!~~~~~<!8$F~<!
                          .x8$$$!~~~~::!~~~~~~~~~~~!!X$$$!!!!MM!!~~~~~!!M$R~~~!
               .::xxxnHW8$$$$$$$$$$$$$$!!~~~~~~~~~~<!@$$X!!!!MM~~~~~<!!X$E~~~~!
          :t$$$$$$$$$$$$$$$$$$$$$$$$$$$!!~~~~~~~~~~!X$$$X~!!!MX~~~~~!!X$$~~~~!!
       ~~~~#R$$$$$RR8$$$$$$$$$$$$$$$$$$!!~~~~~~~~~<!M$$$B~!!!M!~~~~~!X$$!~~~~!!
     ~~~~~~~~?$$$$$$$$$$$$$$$$$$$$$$$$$!!~~~~~~~~~!!$$$$$X!!X$!~~~~!X$$R~~~~<!f
  :~~~~~~~~~`~?$$$$$$$$$$$$$$$$$$$$$$$$!!~~~~~~~~!!X$$$$$$X!M$~~~<!W$$R~~~~~!! 
 ~~~~~~~~~~  ~~M$$$$$$$$$$$$$$$$$$$$$$$!!~~~~~~~~!!M$$$$$$$$$Bid$$$$$$!~~~~~!! 
!~~~~~~~~~~~~~~~$$$$$$$$$$$$$$$$$$$$$$$!~~~~~~~~~!!$$$$$$$$$$$$$$$$$$!~~~~~~!~ 
!~~~~~~~~~~~~~~~M$$$$$$$$$$$$$$$$$$$$$$!:~~~~~~~<!X$$$$$$$$$$$$$$$$$!~~~~~~!!  
~~~~~~~~~~~~~~!!!$$$$$$$$$$$$$$$$$$$$$R!!:~~~~~~!!M$$$$$$$$$$$$$$"XR~~~~~~~!!  
~~~~~~~~~~~~~!!!!$$$$$$$$$$$$$$$$$$$$$R!<!~~~~~!!!X$$$$$$$$$$$P~  !~~~~~~~!!   
~~~~~~~~~~~<!!!!!$$$$$$$$$$$$$$$$$$$$$X!!~~~~~<!!!@#""`           ~~~~~~~~!!   
~~~~~~~~~~~!!!!!X$$$$$$$$$$$$$$$$$$$$$X!~~~~~~!!!                '~~~~~~~!!    
~~~~~~~~~~~<!!!!M$$$$$$$$$$$$$$$$$$$$$X!~~~~~!!!f                '~~~~~~<!!    
~~~~~~~~~~~~~!!!$$$$$$$$$$$$$$$$$$$$$R!~~~~~~!!!                 '~~~~~<!!>    
~~~~~~~~~~~~~~!!M$$$$$$$$$$$$$$$$$$$" !~~~~~!!!!                 ~~~~~~!!!     
~~~~~~~~~~~~~~!!!$$$$$$$$$$$$$$$$$R~ .!~~~~~!!!                  ~~~~~!!!!     
~~~~~~~~~~~~~~~!!!$$$$$$$$$$$$$*?!!!~!!~~~~<!!~                  ~~~~!!!!!     
~~~~~~~~~~~~~~~~!!!$$$$$$$$*"~!!!!!!!!!~~~~!!!                  <~~~:!!!!!     
!~~~~~~~~~~~~~~~~!!M$$$$#~~~~~~~~~~~!!~~~~~!!                   ~~~~~~~!!!     
!<~~~~~~~~~~~~~~~!!!R"~~~~~~~~~~~~~!!!~~~~<!!                  '~~~~~~<!!      
!<~~~~~~~~~~~~~~~~!!!~~~~~~~~~~~~~~!!~~~~~!!!X:                ~~~~~~~!!~      
!!~~~~~~~~~~~~~~~~!!!!~~~~~~~~~~~~<!!~~~~!!!9$MX:              ~~~~~~<!!       
!!!!!~~~~~~~~~~~~~!!!!:~~~~~~~~~~~!!~~~~~!!X$$$X!~            '~~~~~~!!~       
!!!!!!~~~~~~~~~~~<!!!!!!~~~~~~~~~~!!~~~~!!!M$$R!~~~~          ~~~~~~!!!        
!!!!!!!<~~~~~~~~~~~!!!!!!!:<:~~~~~!!~~~~!!X$$R!~~~~~~         ~~~~~~!!         
!!!!!!!!~~~~~~~~~~<!!!!!!!!!!!!!<!!!~~~~!!@$$!~~~~~~~~        ~~~~~!!~         
!!!!!!!!!~~~~~~~~:<!!!!X!!!!!!!!!!!!~~~!!X$$!~~~~~~~~~~~~:   '~~~~~!!          
'!!!!!!!!!!~~~~~~~!!!!!!?!!!!!!!!!!!~~<!!M$M!~~~~~~~~~~~~~~~ '~~~~~!~          
 !!!!!!!!!!\~~~~~~~>!!!!  `"MMMHX!!~~~<!!$R!~~~~~~~~~~~~~~~~~<~~~~!!           
  !!!!!!!!!!<~~~~~<!!!!!   .::<!!!!<~~!!X8X!~~~~~~~~~~~~~~~~~~~~~~!!           
  `X!!!!!!!!~~~~~!<!!!!!!!!!!!!~~!!\~~!!M$MX!:~~~~~~~~~~~~~~~~<!~~!>           
  !X!!!!!!!!~!!:!!!!!!!!!!~!!!:~~!!~~~!!$M!~~!!<~~~~~~~~~~~~~~~!!!!            
  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:!!~~:!9R!~~~~~~!~~~~~~~~~~~~~~<!!f            
 'CHAT!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~!!MX~~~~~~~~~~~~~~~~~~~~~~!!X             
```
After:
```
                                              ''..$$$$$$$$$$662266??MMIIDDEE66  
                                              ''..$$$$$$$$$$662266??MMIIDDEE66  
                                            ''>>$$$$$$<<WWOOOOggPP88,,HH99..;;  
                                            ''>>$$$$$$<<WWOOOOggPP88,,HH99..;;  
                                          ..HH..$$$$EEPP~~ggOOggVV??22..$$$$00!!
                                          ..HH..$$$$EEPP~~ggOOggVV??22..$$$$00!!
                                        99((PP77;;CCII5555VVVV4433WWPP88..<<==66
                                        99((PP77;;CCII5555VVVV4433WWPP88..<<==66
                                      ..!!==MM$$..99DD8899gggg~~ggOOmm88HH@@PP!!
                                      ..!!==MM$$..99DD8899gggg~~ggOOmm88HH@@PP!!
                                      ::88EEMM@@MMPP77BB??gg88~~88__~~88==kkTT88
                                      ::88EEMM@@MMPP77BB??gg88~~88__~~88==kkTT88
                                        ::!!EEHHCCCCEEMM77PPQQ00??nn~~??0000((  
                                        ::!!EEHHCCCCEEMM77PPQQ00??nn~~??0000((  
                                        8888,,00??..BB@@11??PP""ggmmVV55//GG    
                                        8888,,00??..BB@@11??PP""ggmmVV55//GG    
                                        8888,,MM00..HHEE77==((//>>));;$$00))    
                                        8888,,MM00..HHEE77==((//>>));;$$00))    
                                      ""''((,,\\PP~~ggII00!!~~ddXX''88$$;;<<''  
                                      ""''((,,\\PP~~ggII00!!~~ddXX''88$$;;<<''  
                                        VV~~~~~~ggOO99gg..!!88PP((EE::00++..;;((
                                        VV~~~~~~ggOO99gg..!!88PP((EE::00++..;;((
                                      BB~~~~~~~~gg  VVmm--;;!!!!))::,,gg??88CC!!
                                      BB~~~~~~~~gg  VVmm--;;!!!!))::,,gg??88CC!!
                                  11??PP~~~~~~~~~~__~~PP;;::!!!!!!PPPP''PPll@@88
                                  11??PP~~~~~~~~~~__~~PP;;::!!!!!!PPPP''PPll@@88
                                11YYPPgg~~~~~~~~~~~~~~!!..;;!!!!!!!!!!88~~00,,OO
                                11YYPPgg~~~~~~~~~~~~~~!!..;;!!!!!!!!!!88~~00,,OO
                              &&KK~~~~~~gg~~~~~~~~~~FF0000!!,,//!!88VV~~MMEEPP??
                              &&KK~~~~~~gg~~~~~~~~~~FF0000!!,,//!!88VV~~MMEEPP??
                          ::..$$PP~~mm??gg~~~~~~~~gg//..##!!777788~~~~??33OOnn!!
                          ::..$$PP~~mm??gg~~~~~~~~gg//..##!!777788~~~~??33OOnn!!
          <<""&&//NNLL::))$$$$$$$$$$$$##PP~~~~~~~~VV77$$TT!!77hh~~~~((==CC~~gg!!
          <<""&&//NNLL::))$$$$$$$$$$$$##PP~~~~~~~~VV77$$TT!!77hh~~~~((==CC~~gg!!
    88gg~~ggMM$$$$;;))$$$$$$$$$$$$$$$$##PP~~~~~~~~((..$$OO!!;;PP~~gg==00gg~~??22
    88gg~~ggMM$$$$;;))$$$$$$$$$$$$$$$$##PP~~~~~~~~((..$$OO!!;;PP~~gg==00gg~~??22
88mm~~~~~~gg__LL$$$$$$$$$$$$$$$$$$$$$$##PP~~~~~~PP::$$$$$$0066rrAA00$$\\~~~~!!  
88mm~~~~~~gg__LL$$$$$$$$$$$$$$$$$$$$$$##PP~~~~~~PP::$$$$$$0066rrAA00$$\\~~~~!!  
PP~~~~~~~~~~~~~~..$$$$$$$$$$$$$$$$$$$$##mm~~~~~~??00$$$$$$$$$$$$$$$$99~~~~gg88  
PP~~~~~~~~~~~~~~..$$$$$$$$$$$$$$$$$$$$##mm~~~~~~??00$$$$$$$$$$$$$$$$99~~~~gg88  
~~~~~~~~~~~~gg!!##$$$$$$$$$$$$$$$$$$$$::..~~~~gg!!;;$$$$$$$$$$FF""RR~~~~~~88    
~~~~~~~~~~~~gg!!##$$$$$$$$$$$$$$$$$$$$::..~~~~gg!!;;$$$$$$$$$$FF""RR~~~~~~88    
~~~~~~~~~~VV!!!!00$$$$$$$$$$$$$$$$$$$$==gg~~~~((!!))!!00        ""~~~~~~gg!!    
~~~~~~~~~~VV!!!!00$$$$$$$$$$$$$$$$$$$$==gg~~~~((!!))!!00        ""~~~~~~gg!!    
~~~~~~~~~~nn88!!..$$$$$$$$$$$$$$$$$$00FF~~~~PP!!22              $$~~~~nn((((    
~~~~~~~~~~nn88!!..$$$$$$$$$$$$$$$$$$00FF~~~~PP!!22              $$~~~~nn((((    
~~~~~~~~~~~~~~!!..$$$$$$$$$$$$$$$$FF$$PP~~~~!!!!                OO~~~~88!!      
~~~~~~~~~~~~~~!!..$$$$$$$$$$$$$$$$FF$$PP~~~~!!!!                OO~~~~88!!      
~~~~~~~~~~~~~~gg!!##$$$$$$&&::$$))!!88PP~~VV!!88                VV~~??!!!!      
~~~~~~~~~~~~~~gg!!##$$$$$$&&::$$))!!88PP~~VV!!88                VV~~??!!!!      
??~~~~~~~~~~~~~~PP,,//QQgg~~~~~~~~gg!!~~~~??!!                ""~~~~~~??!!      
??~~~~~~~~~~~~~~PP,,//QQgg~~~~~~~~gg!!~~~~??!!                ""~~~~~~??!!      
((~~~~~~~~~~~~~~~~!!88~~~~~~~~~~~~??PP~~gg!!66@@''            OO~~~~nn!!88      
((~~~~~~~~~~~~~~~~!!88~~~~~~~~~~~~??PP~~gg!!66@@''            OO~~~~nn!!88      
!!!!88~~~~~~~~~~nn!!!!??~~~~~~~~~~!!~~~~88::$$<<ggOO          hh~~~~8888        
!!!!88~~~~~~~~~~nn!!!!??~~~~~~~~~~!!~~~~88::$$<<ggOO          hh~~~~8888        
!!!!!!((~~~~~~~~~~??!!!!!!..??PPVV!!~~~~!!88//gg~~~~gg        ~~~~gg88          
!!!!!!((~~~~~~~~~~??!!!!!!..??PPVV!!~~~~!!88//gg~~~~gg        ~~~~gg88          
##!!!!!!88gg~~~~mm((!!//))!!!!!!!!!!~~??::..PP~~~~~~~~~~mmOO$$~~~~PP88          
##!!!!!!88gg~~~~mm((!!//))!!!!!!!!!!~~??::..PP~~~~~~~~~~mmOO$$~~~~PP88          
  !!!!!!!!00nn~~~~FF!!!!  44DD==//??~~((55;;~~~~~~~~~~~~~~~~nn~~~~!!            
  !!!!!!!!00nn~~~~FF!!!!  44DD==//??~~((55;;~~~~~~~~~~~~~~~~nn~~~~!!            
  LL!!!!!!!!ggVV88((!!!!!!88!!VVPPGG~~!!99QQ??VV~~~~~~~~~~~~~~??PP((            
  LL!!!!!!!!ggVV88((!!!!!!88!!VVPPGG~~!!99QQ??VV~~~~~~~~~~~~~~??PP((            
""3366!!!!!!!!!!!!!!!!!!!!!!!!!!''ggVV22RR~~~~~~gg~~~~~~~~~~~~VV//22            
""3366!!!!!!!!!!!!!!!!!!!!!!!!!!''ggVV22RR~~~~~~gg~~~~~~~~~~~~VV//22            
```
[Answer]
# Ruby, ~~180~~ ~~158~~ ~~148~~ ~~128 + 4~~ 124 + 4 = 128 bytes
Run with `$ ruby -nl` (+4 bytes for `-nl` flags). Takes input on STDIN.
```
y,x=x,$_.scan(/..?/)
(puts [x.zip(y).map{|c|(("%2s"*2%c).bytes.reduce(:+)/4.0).round.chr*2}*""]*2
y,x=x,[])if$.%2<1||$<.eof?
```
See it on ideone: <http://ideone.com/brmP3L>
## Ungolfed & explanation
Per `man ruby`, the `-n` flag "[c]auses Ruby to assume the following loop around your script ... `while gets ... end`". The special variable `$_` contains the last line read by `gets`. The `-l` flag removes the `\n` from each line, equivalent to `$_.chop!`.
```
y, x = x, $_.scan(/..?/)
( puts [
    x.zip(y).map {|c|
      (("%2s" * 2 % c).bytes.reduce(:+) / 4.0).round.chr * 2
    } * ""
  ] * 2
  y, x = x, []
) if $. % 2 < 1 || $<.eof?
```
The special variable `$.` is the number of lines that have been read so far, and `$<` is STDIN. The pairs of characters from every second line gets zipped with the previous line's. The format string `%2s%2s` combines the characters and pads it with spaces, then the characters are averaged.
]