Push each file name onto an anonymous array keyed on size, then look for hash keys with multiple values. Something like:

my %files;
foreach my $file_found (readdir(DIR)) {
    # next if $file_found =~ /^\.{1,2}\z/;
    my $size = (stat("$dir/$file_found"))[7];
    $files{$size} ||= [];
    push @{ $files{$size} }, $file_found;
}

foreach my $same_size (values %files) {
    next if @$same_size == 1;
    print join(', ', @$same_size);
}
[download]

Untested. Are you feeling lucky?