Differential cross sections for transitions of known weak strength were measured with the (3He, t) reaction at 420 MeV on targets of 12C, 13C, 18O, 26Mg, 58Ni, 60Ni, 90Zr, 118Sn, 120Sn, and 208Pb. Using these data, it is shown that the proportionalities between strengths and cross sections for this probe follow simple trends as a function of mass number. These trends can be used to confidently determine Gamow-Teller strength distributions in nuclei for which the proportionality cannot be calibrated via beta-decay strengths. Although theoretical calculations in the distorted-wave Born approximation overestimate the data, they allow one to understand the main experimental features and to predict deviations from the simple trends observed in some of the transitions.