We have studied the optical properties of WSe2 monolayers (ML) by means of photoluminescence (PL), PL excitation (PLE) and Raman scattering spectroscopy at room temperature and as a function of hydrostatic pressure up to ca. 12 GPa. For comparison the study comprises two cases: A single WSe2 ML directly transferred onto one of the diamonds of the diamond anvil cell and a WSe2 ML encapsulated into hexagonal boron nitride (hBN) layers. The pressure dependence of the A and B exciton, as determined by PL and PLE, respectively, is very different for the case of the bare WSe2 ML and the hBN/WSe2-ML/hBN heterostructure. Whereas for the latter the A and B exciton energy increases linearly with increasing pressure at a rate of 3.5 to 3.8 meV/GPa, for the bare WSe2ML the A and B exciton energy decreases with a coefficient of -3.1 and -1.3 meV/GPa, respectively. We interpret that this behavior is due to a different stress situation. For a single ML the stress tensor is essentially uniaxial with the compressive stress component in the direction perpendicular to the plane of the ML. In contrast, for the substantially thicker hBN/WSe2/hBN heterostructure the compression is hydrostatic. The results from an analysis of the pressure dependence of the frequency of Raman active modes comply with the interpretation of having a different stress situation in each case.