Given a collection of sets of cardinality at most k, with weights for each
set, the maximum weighted packing problem is that of finding a collection o
f disjoint sets of maximum total weight. We study the worst case behavior o
f the t-local search heuristic for this problem proving a tight bound of k
- 1 + 1/t. As a consequence, for any given r < 1/(k - 1) we can compute in
polynomial time a solution whose weight is at least r times the optimal.