Other monks have already pointed out the bug and offered suggestions. I just want to show that there are more than one way to do it in Perl, depending on, personal taste, I'd say.

# Implementation 1 - the mundane way
sub weighted_hash
{
    my $hashref = shift;
    my @weighted;

    for my $key (keys %$hashref) {
        for (1 .. $hashref->{$key}) {
            push @weighted, $key;
        }
    }
    
    rand_elt @weighted;
}



# Implementation 2 - the perl monk one-liner
sub weighted_hash
{
    my $hashref = shift;

    rand_elt
        map {
            my $key = $_;
            map { $key } 1 .. $hashref->{$key}
        } keys %$hashref;
}
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