We show that the hierarchy between the Planck and the weak scales can follow from the tendency of gravitons and fermions to localize at different edges of a thick double wall embedded in an ${\mathrm{AdS}}_{5}$ spacetime without reflection symmetry. This double wall is a stable BPS thick-wall solution with two subwalls located at its edges; fermions are coupled to the scalar field through Yukawa interactions, but the lack of reflection symmetry forces them to be localized in one of the subwalls. We show that the graviton zero-mode wave function is suppressed in the fermion edge by an exponential function of the distance between the subwalls, and that the massive modes decouple so that Newtonian gravity is recuperated.