We define a notion of unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring R), which is assumed to carry an involution of the form X∗ = Y , R∗ ⊆ R. We prove that a weight module V is unitarizable iff it is isomorphic to its finitistic dual V . Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necess...