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.)