Sort the indices then use an array slice on each array.

knoppix@Microknoppix:~$ perl -E '
> @items = qw{ dog desk cow };
> @weights = qw{ 20 10 150 };
> @sortedIdx = sort { $items[ $a ] cmp $items[ $b ] } 0 .. $#items;
> @items = @items[ @sortedIdx ];
> @weights = @weights[ @sortedIdx ];
> say qq{@items};
> say qq{@weights};'
cow desk dog
150 10 20
knoppix@Microknoppix:~$
[download]

I hope this is helpful.