What I noticed: You keep your input file in memory while you read your abreviations line by line.

Depending on the usual size of those files this might be a good choice.

OTOH: I'd expect an inputfile to be substantially larger than your abreviations.

if so you might want to consider to keep the abreviations in memory and to loop over the input lines:

# UNTESTED!
use strict;
use warnings;

   open( ABB, '<', 'jabb.txt' ) or die "Couldn't open ABB.\n$!";
   open( IN, '<', 'input.txt' ) or die "Couldn't open infile.\n$!";
   open( OUT, '>', 'output.out' ) or die "Couldn't open outfile.\n$!";
   
   # prepare abreviations
   my %abb;
   while(<ABB>){
      # there are shorter ways to do it, but to keep your code...
      if(/(.*?)\t(.*?)\n/) {
          $abb{$2}= $1
      }
   }
   close ABB;

   # build a RE for quickly(?) finding abbreviatable words.
   my $abbre= join('|', map "\Q$_\E",keys %abb);
   $abbre= qr/\b($abbre)\b/;

   # replace
   my @myin = <IN>;
   while(<IN>){
      s/$abbre/$abb{$1}/g;
      print OUT; 
   }
   close IN;
   close OUT;
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Update: Thanks to Zaxo's obfu-entry ;-) below I noticed I forgot to escape the list of abbreviatable words.