We have used in situ polar Kerr effect measurements to study the magnetic anisotropy of MBE-grown X/Co/Y trilayers, where X and Y are combinations of the nonmagnetic metals Ag, Au, Cu, or Pd. The competition between the perpendicular anisotropy of the initial underlayer X/Co interface and the in-plane shape anisotropy of the Co film allows us to adjust the total anisotropy of the uncovered Co to be in plane and of moderate strength. In this way, we can measure hard-axis (perpendicular) polar hysteresis curves in situ as a function of overlayer Y coverage, and directly deduce the anisotropy field. Polar hysteresis curves were measured in situ for systematically varied Co and overlayer Y layer thicknesses 2 angstrom less-than-or-equal-to t(Co) less-than-or-equal-to 20 angstrom and 0 angstrom less-than-or-equal-to t(Y) less-than-or-equal-to 100 angstrom. We find, for particular combinations, the magnitude of the X/Co/Y perpendicular anisotropy is strongly peaked at approximately 1 atomic layer overlayer Y coverage.