I'm no probabalist, but your code seems on the ball to me. Here's an alternative method I use from time to time that doesn't require the creation of an additional accumulating-weight array:

sub choose_weighted {
    my $weights  = shift;
    my $total    = 0;

    $total += $_ for @$weights;

    my $rand_val = $total * rand;
    my $i        = -1;

    $rand_val -= $weights->[++$i] while ($rand_val > 0);

    return $i;
}
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1. Pick a random number less than the total
2. At each position of the array, subtract the weight at that position
3. When the result is negative, return that position

I have found this algorithm easier to adapt for multiple selections, i.e., calling choose_weighted( [1.75, 2, 3.6, 4], 2 ) and getting back two (different) numbers randomly chosen with this weighting. However, once you start doing this, you have to modify the array of weights (each time you select an item, set its weight to zero and subtract accordingly from $total), which may be undesired here.

Cheers,

blokhead