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.
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