  Atomically thin transition metal dichalcogenides (TMDCs) such as MoS$_2$ and
WSe$_2$ are emerging as a new platform for exploring many-body effects. Coulomb
interactions are markedly enhanced in these materials because of the reduced
screening and the large Wigner-Seitz radii. Although many-body excitonic
effects in TMDCs have been extensively studied by optical means, not until
recently did probing their strongly correlated electronic effects become
possible in transport. Here, in p-type few-layer WSe$_2$ we observe highly
density-dependent quantum Hall states of {\Gamma} valley holes below 12 T,
whose predominant sequences alternate between odd- and even-integers. By
tilting the magnetic field to induce Landau level crossings, we show that the
strong Coulomb interaction enhances the Zeeman-to-cyclotron energy ratio from
2.67 to 3.55 as the density is reduced from 5.7 to 4.0$\times$10$^{12}$
cm$^{-2}$, giving rise to the even-odd alternation. Unprecedentedly, this
indicates a 4.8 times enhancement of the g-factor over its band theory value at
a density as high as 4.0$\times$10$^{12}$ cm$^{-2}$. Our findings unambiguously
demonstrate that p-type few-layer WSe$_2$ is a superior platform for exploring
strongly correlated electronic phenomena, opening a new perspective for
realizing the elusive Wigner crystallization at a moderate density.
