This may not be as slick as other answers, but I thought I'd offer it. This one is a "fix up" code, as opposed to maintenance code.

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

my %hash = (
    AA=>1,
    AB=>5,
    AC=>7,
    AD=>3,
    AE=>4,
    BA=>2,
    BB=>4,
    BC=>16,
    BD=>21,
    ZA=>12,
    ZB=>1,
    ZC=>3,
    ZY=>2,
    ZZ=>2, );

my %newhash=();

for ( sort keys %hash ) {
    next if defined $newhash{sym_index($_)};
    if ( defined($hash{reverse($_)}) ) {
        $newhash{sym_index($_)} = $hash{$_} + $hash{reverse ($_)};
    }
    else {
        $newhash{sym_index($_)} = $hash{$_};
    }
}

for ( sort keys %newhash ) {
    print $_, " => ", $newhash{$_}, "\n";
}

sub sym_index {
    my $a = shift;
    return $a if ( $a le reverse( $a ) );
    return reverse( $a );
}
[download]

And results are:

C:\Code>perl symmetrize.pl
AA => 2
AB => 7
AC => 7
AD => 3
AE => 4
AZ => 12
BB => 8
BC => 16
BD => 21
BZ => 1
CZ => 3
YZ => 2
ZZ => 4
[download]

Update: cleaner output