We present a strategic network formation model based on membership in clubs. Individuals choose affiliations. The set of all memberships induces a weighted network where two individuals are directly connected if they share a club. Two individuals may also be indirectly connected using multiple memberships of third parties. Individuals gain from their position in the induced network and pay membership fees. We study the club congestion model where the weight of a link decreases with the size of the smallest shared club. A trade-off emerges between the size of clubs, the depreciation of indirect connections, and the membership fee.