Memory consumption seems to be about 50% of your solution or less, with the running time being the same or a bit shorter.

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

use List::Util qw{ sum };

my %h;
$/ = q();
while (my $block = <>) {
    my @lines = split /\n/, $block;
    my $key = $lines[1];
    my ($count) = $lines[3] =~ /\s(\d+)/;
    unless (exists $h{$key}) {
        $block =~ s/\n\n?$//;
        $block =~ s/\s*\d+$//;
        $h{$key} = $block;
    }
    $h{$key} .= "\t$count";
}

for my $key (sort keys %h) {
    my ($match) = $h{$key} =~ /((?:\d+\t*)+)$/;
    my @counts = $match =~ /\d+/g;
    my $sum = sum(@counts);
    say join "\t", $h{$key}, "count:$sum\n";
}
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If you're interested, here's how I created the input data:

#!/usr/bin/perl
use warnings;
use strict;

my ($n, $size, $dna_length) = @ARGV;

my $template = << '__EOT__';
@ns
%s
+
//%s    %d
__EOT__

open my $OUT, '>', "file$n" or die $!;
for my $i (1 .. $size) {
    my $dna = join q(), map qw( A C G T )[ rand 4 ], 1 .. $dna_length;
    my $ignored = join q(), map +('A' .. 'Z')[ rand 26 ], 1 .. 4;
    my $count = 1 + int rand 20;
    printf {$OUT} $template, $dna, $ignored, $count;
    print {$OUT} "\n" unless $i == $size;
}
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#!/bin/bash
for i in {000..999} ; do
    create-file $i 10000 6
done
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($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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