High quality WSe2 films have been grown on bilayer graphene (BLG) with layer-by-layer control of thickness using molecular beam epitaxy. The combination of angle-resolved photoemission, scanning tunneling microscopy/spectroscopy, and optical absorption measurements reveal the atomic and electronic structures evolution and optical response of WSe2/BLG. We observe that a bilayer of WSe2 is a direct bandgap semiconductor, when integrated in a BLG-based heterostructure, thus shifting the direct-indirect band gap crossover to trilayer WSe2. In the monolayer limit, WSe2 shows a spin-splitting of 475 meV in the valence band at the K point, the largest value observed among all the MX2 (M = Mo, W; X = S, Se) materials. The exciton binding energy of monolayer-WSe2/BLG is found to be 0.21 eV, a value that is orders of magnitude larger than that of conventional three-dimensional semiconductors, yet small as compared to other two-dimensional transition metal dichalcogennides (TMDCs) semiconductors. Finally, our finding regarding the overall modification of the electronic structure by an alkali metal surface electron doping opens a route to further control the electronic properties of TMDCs.