It is about that 'next' statement. I commented out your next statement, and replaced it with mine:

use strict;
use warnings;
my %bucket = (
    key1 => {'1' => 3},
    key2 => {'1' => 3,
                 '2' => 2},
    key3 => {'1' => 11,
                 '2' => 36}
      );

my %spair = ();
my $cnt =0;

foreach my $kmer ( keys %bucket  ) {
   foreach my $si (keys %{$bucket{$kmer}}) {     
      foreach my $sn (keys %{$bucket{$kmer}}) { 
#        next if ($spair{$sn."-".$si} != 0);
         next if ($sn < $si);
         if ( $si == $sn ) {
            $cnt = $bucket{$kmer}{$si};
         } else {
            $cnt = $bucket{$kmer}{$si}*$bucket{$kmer}{$sn};
         }
         $spair{$si."-".$sn} +=$cnt; 
      }
   }     # ----- end foreach ----- 
}  # ----- end foreach -----

use Data::Dumper;
print Dumper \%spair;
[download]

Here is the result:

$VAR1 = {
          '1-1' => 17,
          '2-2' => 38,
          '1-2' => 402
        };
[download]