Excitons in monolayer semiconductors such as MoS2 are strongly confined in the layer plane with minimal freedom to orient themselves in the out-of-plane direction. Recent gated spectroscopy measurements have suggested that this may not be the case. However, there is a large discrepancy in the experimental and theoretical polarizability values. Here we investigate the out-of-plane polarizability of excitons in monolayer WSe2 up to large electric fields of ~1.5 V/nm using double-gate photoluminescence spectroscopy and electroabsorption spectroscopy. The double gate configuration allows us to indepdnently control the doping level and the vertical electric field while avoiding unintentional laser-induced photo-doping effects. We find that the photo-doping density increases linearly with vertical electric fields due to interfacial charge traps even when the sample is encapsulated in hexagonal boron nitride (hBN) crystals. We show that neutral excitons exhibit negligible Stark shift contrary to the earlier experimental observations. On the other hand, charged exciton energy was found to exhibit small but linear Stark shift suggesting the presence of permanent dipole moment.