Layer-by-layer graphene growth is demonstrated by repeating CVD growth cycles directly on sapphire substrates. Improved field-effect mobility values are observed for the bottom-gate transistors fabricated by using the bilayer graphene channel, which indicates an improved crystallinity is obtained after the second CVD growth cycle. Despite the poor wettability of copper on graphene surfaces, graphene may act as a thin and effective diffusion barrier for copper atoms. The low resistivity values of thin copper films deposited on thin monolayer MoS2/monolayer graphene heterostructures have demonstrated its potential to replace current thick liner/barrier stacks in back-end interconnects. The unique van der Waals epitaxy growth mode will be helpful for both homo- and heteroepitaxy on 2D material surfaces.