The evolution in the surface morphology of epitaxial graphene films and 6H-SiC(0001) substrates is studied by electron channeling contrast imaging. Whereas film thickness is determined by growth temperature only, increasing growth times at constant temperature affect both internal stress and film morphology. Annealing times in excess of 8-10 minutes lead to an increase in the mean square roughness of SiC step edges to which graphene films are pinned, resulting in compressively stressed films at room temperature. Shorter annealing times produce minimal changes in the morphology of the terrace edges and result in nearly stress-free films upon cooling to room temperature.