Moiré superlattices constructed from transition metal dichalcogenides have demonstrated a series of emergent phenomena, including moiré excitons, flat bands, and correlated insulating states. All of these phenomena depend crucially on the presence of strong moiré potentials, yet the properties of these moiré 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/WSe2 moiré superlattice and graphene/WS2/WSe2 trilayer heterostructure. Our experiments reveal that the hybridization between moiré bands in WS2/WSe2 exhibits an unusually large momentum dependence, with the splitting between moiré 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/WSe2 superlattice can imprint an unexpectedly large moiré potential on a third, separate layer of graphene (g/WS2/WSe2), suggesting new avenues for engineering two-dimensional moiré superlattices.