We demonstrate that tunable attractive (bonding) and repulsive (anti-bonding) forces can arise in highly asymmetric structures coupled to external radiation, a consequence of the bonding/anti-bonding level repulsion of guided-wave resonances that was first predicted in symmetric systems. Our focus is a geometry consisting of a photonic-crystal (holey) membrane suspended above an unpatterned layered substrate, supporting planar waveguide modes that can couple via the periodic modulation of the holey membrane. Asymmetric geometries have a clear advantage in ease of fabrication and experimental characterization compared to symmetric double-membrane structures. We show that the asymmetry can also lead to unusual behavior in the force magnitudes of a bonding/antibonding pair as the membrane separation changes, including nonmonotonic dependences on the separation. We propose a computational method that obtains the entire force spectrum via a single time-domain simulation, by Fourier-transforming the response to a short pulse and thereby obtaining the frequency-dependent stress tensor. We point out that by operating with two, instead of a single frequency, these evanescent forces can be exploited to tune the spring constant of the membrane without changing its equilibrium separation.