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Scanning tunneling microscopy (STM) at 5 K is used to study WSe2 layers grown on epitaxial graphene which is formed on Si-terminated SiC(0 0 0 1). Specifically, a partial hydrogenation process is applied to intercalate hydrogen at the SiC-graphene interface, yielding areas of quasi-free-standing bilayer graphene coexisting with bare monolayer graphene. We find that an abrupt and structurally perfect homojunction (band-edge offset ∼0.25 eV) is formed when WSe2 overgrows a lateral junction between adjacent monolayer and quasi-free-standing bilayer areas in the graphene. The band structure modulation in the WSe2 overlayer arises from the varying work function (electrostatic potential) of the graphene beneath. Scanning tunneling spectroscopy measurements reveal that this effect can be also utilized to create WSe2 quantum dots that confine either valence or conduction band states, in agreement with first-principles band structure calculations.