The weak tensor product was introduced by Snevily as a way to construct new graphs that admit a-labelings from a pair of known a-graphs. In this article, we show that this product and the application to a-labelings can be generalized by considering as a second factor of the product, a family G of bipartite (p, q)-graphs, p and q fixed. The only additional restriction that we should consider is that for every F ¿ G , there exists an a-labeling fF with fF (V(F )) = L¿H, where L, H ¿ [0, q] are the stable sets induced by the characteristic of fF and they do not depend on F .Wealso obtain analogous applications to near a-labelings and bigraceful labelings.