Interest in two-dimensional (2D) transition-metal dichalcogenides (TMDs) has prompted some recent efforts to grow ultrathin layers of these materials epitaxially using molecular-beam epitaxy (MBE). However, growths of monolayer (ML) and bilayer (BL) WSe 2—an important member of the TMD family—by the MBE method remain uncharted, probably because of the difficulty in generating tungsten fluxes from the elemental source. In this work, we present a scanning tunneling microscopy and spectroscopy (STM/S) study of MBE-grown WSe 2 ML and BL, showing atomically flat epifilm with no domain boundary (DB) defect. This contrasts epitaxial MoSe 2 films grown by the same method, where a dense network of the DB defects is present. The STS measurements of ML and BL WSe 2 domains of the same sample reveal not only the bandgap narrowing upon increasing the film thickness from ML to BL, but also a band-bending effect across the boundary (step) between ML and BL domains. This band-bending appears to be dictated by the edge states at steps of the BL islands. Finally, comparison is made between the STS-measured electronic bandgaps with the exciton emission energies measured by photoluminescence, and the exciton binding energies in ML and BL WSe 2 (and MoSe 2) are thus estimated.