The possible dependence of fundamental couplings and mass ratios on the gravitational potential has been bounded by comparing atomic clock frequencies over Earth's elliptical orbit. Here we evaluate bounds on such dependence from E"otv"os-type experiments that test the Weak Equivalence Principle, including previously neglected contributions from nuclear binding energy. We find that variations of fundamental parameters correlated with the gravitational potential are bounded at 10^-8--10^-9, an improvement of 2--3 orders of magnitude over atomic clock bounds.

To be published (Phys.Rev.Lett.), minor changes and corrections, equivalent to journal version