  Due to high binding energy and oscillator strength, excitons in thin flakes
of transition metal dichalcogenides constitute a perfect foundation for
realizing a strongly coupled light-matter system. In this paper we investigate
mono- and few-layer WSe$_2$ flakes encapsulated in hexagonal boron nitride and
incorporated into a planar dielectric cavity. We use an open cavity design
which provides tunability of the cavity mode energy by as much as 150 meV. We
observe a strong coupling regime between the cavity photons and the neutral
excitons in direct-bandgap monolayer WSe$_2$, as well as in few-layer WSe$_2$
flakes exhibiting indirect bandgap. We discuss the dependence of the exciton's
oscillator strength and resonance linewidth on the number of layers and predict
the exciton-photon coupling strength.
