$ for i in A B C; do echo -e "\n*** $i"; cat $i; echo '----';  cat -vet $i; done

*** A
foo     73
bar     35
word    27
blah    23
----
foo^I73$
bar^I35$
word^I27$
blah^I23$

*** B
bar     35
yada    3
word    27
blah    23
----
bar^I35$
yada^I3$
word^I27$
blah^I23$

*** C
foo     73
word    27
blah    23
life    42
----
foo^I73$
word^I27$
blah^I23$
life^I42$

##</code><code>##

#!/usr/bin/env perl

use strict;
use warnings;
use autodie;

my @in_files = qw{A B C};
my $outfile = 'merge_count.out';
my %data;
my $out_fmt = "%s\t%d\n";

for my $infile (@in_files) {
    open my $fh, '<', $infile;

    while (<$fh>) {
        my ($word, $count) = split;
        $data{$word} += $count;
    }
}

open my $fh, '>', $outfile;

for my $key (sort { $data{$a} <=> $data{$b} } keys %data) {
    printf $fh $out_fmt, $key, $data{$key};
}

##</code><code>##

$ cat merge_count.out
yada    3
life    42
blah    69
bar     70
word    81
foo     146

$ cat -vet merge_count.out
yada^I3$
life^I42$
blah^I69$
bar^I70$
word^I81$
foo^I146$