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 of disjoint sets of maximum total weight. We study the worst case behavior of the $t$-local search heuristic for this problem proving a tight bound of $k-1+{1\over t}$. This continues the work of Hurkens and Schrijver for unweighted packing problems. (Joint work with Esther M. Arkin.)