Let v be a weight sequence on Z and let ψ, ϕ be complex-valued functions on Z such that ϕ (Z) ⊂ Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators C ψ,ϕ on predual Banach spaces c 0 (Z, 1/v) and dual Banach spaces ∞ (Z, 1/v) of Beurling algebras 1 (Z, v).