  We report magneto-absorption spectroscopy of gated WSe$_2$ monolayers in high
magnetic fields up to 60~T. When doped with a 2D Fermi sea of mobile holes,
well-resolved sequences of optical transitions are observed in both
$\sigma^\pm$ circular polarizations, which unambiguously and separately
indicate the number of filled Landau levels (LLs) in both $K$ and $K'$ valleys.
This reveals the interaction-enhanced valley Zeeman energy, which is found to
be highly tunable with hole density $p$. We exploit this tunability to align
the LLs in $K$ and $K'$, and find that the 2D hole gas becomes unstable against
small changes in LL filling and can spontaneously valley-polarize. These
results cannot be understood within a single-particle picture, highlighting the
importance of exchange interactions in determining the ground state of 2D
carriers in monolayer semiconductors.
