In this talk I will discuss some of my recent joint work with Rupert Levene (Dublin) and Stephen Power (Lancaster) on the non-selfadjoint operator algebras generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs. These algebras may be viewed as noncommutative generalisations of weighted Bergman space algebras, or as weighted versions of the free semigroupoid algebras of directed graphs. We obtain a complete description of the commutant in terms of underlying graph and weight structures, together with broad conditions that ensure the double commutant property holds, and we show that this property can fail even in the case of the single vertex graph with two edges and suitable choice of weights.