My current program demonstrates this very well.

Could you show us that program, or at least a short version of it? (SSCCE) Also, this sounds like a case where you might benefit from a test-first approach: even if you don't have the body of your function yet, you can still write tests using Test::More to test this hypothetical function. Not only will it help you see how close you're getting while you're developing, it'll help us understand your problem description better :-)

use warnings;
use strict;
use Test::More;

sub my_func {
    my $target = shift;
    my @weights = @_;
    my @output = (); # TODO!
    return \@output;
}

is_deeply my_func(30, 7,10,13), [10,10,10];
is_deeply my_func( 5,  3,7,11), [3,3];
# TODO: lots more test cases!

done_testing;
[download]

If it were all in whole numbers it would be trivial.

In my experience integers are much easier to work with, and you don't suffer from floating-point imprecisions. I'd suggest switching to milligrams, micrograms, etc. - for example, my Perl (64 bit) can handle integers up to 9007199254740992 without loss of precision. (source)