  In this work, low-energy electron microscopy is employed to probe structural
as well as electronic information in few-layer WSe$_2$ on epitaxial graphene on
SiC. The emergence of unoccupied states in the WSe$_2$--graphene
heterostructures are studied using spectroscopic low-energy electron
reflectivity. Reflectivity minima corresponding to specific WSe$_2$ states that
are localized between the monolayers of each vertical heterostructure are shown
to reveal the number of layers for each point on the surface. A theory for the
origin of these states is developed and utilized to explain the experimentally
observed featured in the WSe$_2$ electron reflectivity.
