Moire superlattices constructed from transition metal dichalcogenides have demonstrated a series of emergent phenomena, including moire excitons, flat bands, and correlated insulating states. All of these phenomena depend crucially on the presence of strong moire potentials, yet the properties of these moire potentials, and the mechanisms by which they can be generated, remain largely open questions. Here, we use angle-resolved photoemission spectroscopy with submicron spatial resolution to investigate an aligned WS2/WSe2moire superlattice and graphene/WS2/WSe2trilayer heterostructure. Our experiments reveal that the hybridization between moire bands in WS2/WSe2exhibits an unusually large momentum dependence, with the splitting between moire bands at the γ point more than an order of magnitude larger than that at K point. In addition, we discover that the same WS2/WSe2superlattice can imprint an unexpectedly large moire potential on a third, separate layer of graphene (g/WS2/WSe2), suggesting new avenues for engineering two-dimensional moire superlattices.