A graph G is weakly gamma -closed if every induced subgraph of G contains one vertex v such that for each non-neighbor u of v it holds that vert N(u)cap N(v) vert <gamma . The weak closure gamma (G) of a graph, recently introduced by Fox et al. (SIAM J Comput 49(2):448–464, 2020), is the smallest number such that G is weakly gamma -closed. This graph parameter is never larger than the degeneracy (plus one) and can be significantly smaller. Extending the work of Fox et al. (2020) on clique enumeration, we show that several problems related to finding dense subgraphs, such as the enumeration of bicliques and s-plexes, are fixed-parameter tractable with respect to gamma (G). Moreover, we show that the problem of determining whether a weakly gamma -closed graph G has a subgraph on at least k vertices that belongs to a graph class mathcal {G} which is closed under taking subgraphs admits a kernel with at most gamma k^2 vertices. Finally, we provide fixed-parameter algorithms for Independent Dominating Set and Dominating Clique when parameterized by gamma +k where k is the solution size. Furthermore, we show that Independent Dominating Set does not admit a polynomial kernel for constant gamma under standard assumptions.