Relation algebras are abstractions of collections of binary relations under the operations of union, intersection, complementation, relational composition, inversion, and identity. A relation algebra is called representable if it is isomorphic to such a collection of relations. An algebra is called weakly representable if it is isomorphic to a collection of relations not necessarily closed under union and complementation. We consider weak representations over finite sets and note a connection between weak representations and relativizations. We also consider the question from Bjarni Jonsson's 1959 paper, whether the class of weakly representable relation algebras forms a variety. We show that it is, provided that a certain embedding condition obtains. Remaining open questions are collected in the concluding remarks.