We report 65 T magnetoabsorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor WSe2. The strongly field-dependent and distinct energy shifts of the 2s, 3s, and 4s excited neutral excitons permits their unambiguous identification and allows for quantitative comparison with leading theoretical models. Both the sizes (via low-field diamagnetic shifts) and the energies of the ns exciton states agree remarkably well with detailed numerical simulations using the nonhydrogenic screened Keldysh potential for 2D semiconductors. Moreover, at the highest magnetic fields, the nearly linear diamagnetic shifts of the weakly bound 3s and 4s excitons provide a direct experimental measure of the exciton’s reduced mass mr=0.20±0.01m0.