Societies change through time, entailing changes in behaviors and institutions. We ask how social change occurs when behaviors and institutions are interdependent. We model a group-structured society in which the transmission of individual behavior occurs in parallel with the selection of group-level institutions. We consider a cooperative behavior that generates collective benefits for groups but does not spread between individuals on its own. Groups exhibit institutions that increase the diffusion of the behavior within the group, but also incur a group cost. Groups adopt institutions in proportion to their fitness. Finally, cooperative behavior may also spread globally. As expected, we find that cooperation and institutions are mutually reinforcing. But the model also generates behavioral source-sink dynamics when cooperation generated in institutional groups spreads to non-institutional groups, boosting their fitness. Consequently, the global diffusion of cooperation creates a pattern of institutional free-riding that limits the evolution of group-beneficial institutions. Our model suggests that, in a group-structured society, large-scale change in behavior and institutions (i.e. social change) can be best achieved when the two remain correlated, such as through the spread successful pilot programs.