In the presence of a monoidal right adjoint G : V -> U between locally finitely presentable symmetric monoidal categories, we examine the behavior of V-Grothendieck topologies on a V-category C, and that of their constituent covering sieves, under the change of enriching category induced by G. We prove in particular that when G is faithful and conservative, any V-Grothendieck topology on C corresponds uniquely to a U-Grothendieck topology on G_*C, and that when G is fully faithful, base change commutes with enriched sheafification in the sense of Borceux-Quinteiro.