  We report a study of the quantum Hall states (QHSs) sequence of holes in
mono- and bilayer WSe$_2$. The QHSs sequence transitions between predominantly
even and predominantly odd filling factors as the hole density is tuned in the
range $1.6 - 12\times10^{12}$ cm$^{-2}$. The QHSs sequence is insensitive to
the transverse electric field, and tilted magnetic field measurements reveal an
insensitivity of the QHSs sequence to the in-plane magnetic field, evincing
that the hole spin is locked perpendicular to the WSe$_2$ plane. These
observations imply that the QHSs sequence is controlled by the
Zeeman-to-cyclotron energy ratio, which remains constant as a function of
perpendicular magnetic field at a fixed carrier density, but changes as a
function of density due to strong electron-electron interaction.
