  We report 65 tesla magneto-absorption spectroscopy of exciton Rydberg states
in the archetypal monolayer semiconductor WSe$_2$. 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 non-hydrogenic 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, $m_r = 0.20 \pm
0.01~m_0$.
