  We have performed high-field magnetization and ESR measurements on
Ba$_3$CoSb$_2$O$_9$ single crystals, as a representative two-dimensional
spin-1/2 Heisenberg antiferromagnet on a uniform triangular lattice, and have
determined all the magnetic parameters. For an applied magnetic field $H$
parallel to the $ab$-plane, the entire magnetization curve including the
plateau at one-third of the saturation magnetization ($M_\mathrm{s}$) is in
excellent agreement with the results of theoretical calculations except an
anomaly near $(3/5)M_\mathrm{s}$, indicative of an additional field-induced
transition. However, for $H\,{\parallel}\,c$, the magnetization curve exhibits
a cusp near $M_\mathrm{s}/3$. Paramagnetic resonance signals above the N\'eel
temperature indicate the nearly isotropic $g$-factor. A detailed analysis of
the collective ESR modes observed in the ordered state, combined with the
magnetization process, provides evidence of the weak easy-plane anisotropy.
