Hmmm... Not totally sure this'll give me the right weighting. But it has inspired me to write:-

use List::Util qw(sum);
my $total = sum values %$group;

my $rnd = rand( $total );
my $runningtot = 0;

foreach ( keys %$group ) {
    
    if ( $rnd > $runningtot && $rnd <= ( $runningtot + $group->{$_} ) 
+) {
        $picked = $_;
        last;
    }#if

    $runningtot += $group->{$_};

}#foreach
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rand() is only called once. No array is made. Straight forward if and a last to drop out once found. Haven't tested for efficiency but I'm guessing it's pretty good.

Lyle