Two-dimensional tungsten diselenide (WSe2) has been used as a component in atomically thin photovoltaic devices, field effect transistors, and tunneling diodes in tandem with graphene. In some applications it is necessary to achieve efficient charge transport across the interface of layered WSe2-graphene, a semiconductor to semimetal junction with a van der Waals (vdW) gap. In such cases, band alignment engineering is required to ensure a low-resistance, ohmic contact. In this work, we investigate the impact of graphene electronic properties on the transport at the WSe2-graphene interface. Electrical transport measurements reveal a lower resistance between WSe2 and fully hydrogenated epitaxial graphene (EG(FH)) compared to WSe2 grown on partially hydrogenated epitaxial graphene (EGPH). Using low-energy electron microscopy and reflectivity on these samples, we extract the work function difference between the WSe2 and graphene and employ a charge transfer model to determine the WSe2 carrier density in both cases. The results indicate that WSe2-EG(FH) displays ohmic behavior at small biases due to a large hole density in the WSe2, whereas WSe2-EG(PH) forms a Schottky barrier junction.