Something like this:

use warnings;
use strict;

chomp(my @data_array=<DATA>);

print join $/ => map{$_->[0]}
      sort{$a->[1] <=> $b->[1]}
      map{[$_,(split/\s+/,$_,2)[1]]} @data_array;

__DATA__
AA 34
AB 22
AC 12
[download]

..produces..

AC 12
AB 22
AA 34
[download]

Update: And if the above is using too much power :), you can simply use a hash like so:

my %hash;

 while(<DATA>){
  next if /^\s*$/;
  my @data = split;
  $hash{$data[1]} = $data[0]
}

  print $hash{$_},' ',$_,$/ for sort{$a<=>$b} keys %hash;

__DATA__
AA 34

AB 22

AC 12
[download]

Update 2: On the Hash method:
Please note that the keys used in the hash must be UNIQUE for the hash method to work properly as intended.
ww thanks for catching that.