Summary: Let \(R\) be a commutative noetherian ring with non-zero identity, \(\mathfrak a\) an ideal of \(R\) and \(M,N\) two \(R\)-modules. The main purpose of this paper is to study the circumstances under which, for fixed integers \(j\in\mathbb N_0\) and \(n\in\mathbb N\), the \(R\)-modules \(\mathrm{Ext}^j_R (N,H^n_{\mathfrak a}(M))\) and \(\mathrm{Tor}^j_R (N,H^n_{\mathfrak a}(M))\) are weakly Laskerian or Matlis reflexive. In this way, we also get to some results about the associated primes, coassociated primes and Bass numbers of \(H^n_{\mathfrak a}(M)\).