I just generated a 5 million line file that approximates your format:

#! perl -slw
use strict;

for( 1 .. 5e6 ) {
    my $n1 = int( rand 100 );
    my $n2 = int( rand 1e6 );

    printf "w\t%d\t%d\t75\t75M\t0\n", $n1, $n2;
    printf "c\t%d\t%d\t75\t75M\t0\n", $n1, $n2 - int( rand 1000 ) + 50
+0;

}
__END__
C:\test>head 1166792.dat
w       70      437286  75      75M     0
c       70      437579  75      75M     0
w       50      852386  75      75M     0
c       50      852473  75      75M     0
w       45      45196   75      75M     0
c       45      45695   75      75M     0
w       83      1739    75      75M     0
c       83      1590    75      75M     0
w       31      838500  75      75M     0
c       31      838902  75      75M     0
[download]

And wrapped your posted snippet up to allow it to run:

#! perl -slw
use strict;

open my $IN2, '<', '1166792.dat' or die $!;

my( %store, %Tally );

while (<$IN2>) {
    chomp $_;
    next if eof;
    my @F2      = split( "\t", $_ );          #Split each tab-delimite
+d field
    my $partner = <$IN2>;
    my @F3      = split( "\t", $partner );    #Split each tab-delimite
+d field
    $store{ ( abs( $F2[2] - $F3[2] ) + 1 ) }++;
    ( $F2[2], $F3[2] ) = ( $F3[2], $F2[2] ) if $F2[2] > $F3[2];
    $Tally{ $F2[1] }{ $F2[2] }{ $F3[2] }++;
}

foreach my $key ( sort { $a <=> $b } keys %store ) {
    print "$key\t$store{$key}\n";
}

foreach my $chr ( sort { $a <=> $b } keys %Tally ) {
    foreach my $value1 ( sort { $a <=> $b } keys %{ $Tally{$chr} } ) {
        foreach my $value2 ( sort { $a <=> $b } keys %{ $Tally{$chr}{$
+value1} } ) {
            print "$chr\t$value1\t$value2\t$Tally{$chr}{$value1}{$valu
+e2}\n";
        }
    }
}
[download]

And it runs to completion under 5.22 using just under 1.2GB.

Unless you're on a very memory constrained system, memory isn't the problem. Do you have somewhere you can post your failing datafile (zipped.)?