further to my previous post (http://www.perlmonks.org/?node_id=1198575), this is another version of my program which seem to produce results more in line with what you seem to be expecting (assuming I have understood what you're expecting). Or, at least, the number of output lines seems to be what you're looking for.

use strict;
use warnings;


my @list = (0, 2, 3);
for my $w (1, 2, 3, 4, 7, 8) {
    print "count = $w\n";
    make_sets2($w, "", @list);
}

sub make_sets2 {
    my $weight = shift;
    my $temp_result = shift;
    print "$temp_result\n" and return if $weight <= 0;
    while (@_) {
        my $item = shift;
        make_sets2( $weight -1, "$temp_result$item, ", ($item, @_));
    }
}
[download]

$ time perl  multisets.pl
count = 1
0,
2,
3,
count = 2
0, 0,
0, 2,
0, 3,
2, 2,
2, 3,
3, 3,
count = 3
0, 0, 0,
0, 0, 2,
0, 0, 3,
0, 2, 2,
0, 2, 3,
0, 3, 3,
2, 2, 2,
2, 2, 3,
2, 3, 3,
3, 3, 3,
count = 4
0, 0, 0, 0,
0, 0, 0, 2,
0, 0, 0, 3,
0, 0, 2, 2,
0, 0, 2, 3,
0, 0, 3, 3,
0, 2, 2, 2,
0, 2, 2, 3,
0, 2, 3, 3,
0, 3, 3, 3,
2, 2, 2, 2,
2, 2, 2, 3,
2, 2, 3, 3,
2, 3, 3, 3,
3, 3, 3, 3,
count = 7
0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 2,
0, 0, 0, 0, 0, 0, 3,
0, 0, 0, 0, 0, 2, 2,
. . . (abbreviated)
2, 2, 2, 3, 3, 3, 3, 3,
2, 2, 3, 3, 3, 3, 3, 3,
2, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3,

real    0m0.048s
user    0m0.015s
sys     0m0.000s
[download]

$ time perl  multisets.pl > /dev/null

real    0m0.043s
user    0m0.000s
sys     0m0.031s
[download]