We use a van der Waals pickup technique to fabricate different heterostructures containing WSe 2 (WS 2 ) and graphene. The heterostructures were structured by plasma etching, contacted by one-dimensional edge contacts, and a top gate was deposited. For graphene/WSe 2 /SiO 2 samples we observe mobilities of ∼12 000 cm 2 V −1 s −1 . Magnetic-field-dependent resistance measurements on these samples show a peak in the conductivity at low magnetic fields. This dip is attributed to the weak antilocalization (WAL) effect, stemming from spin-orbit coupling. Samples where graphene is encapsulated between WSe 2 (WS 2 ) and hexagonal boron nitride show a much higher mobility of up to ∼120 000 cm 2 V −1 s −1 . However, in these samples no WAL peak can be observed. We attribute this to a transition from the diffusive to the quasiballistic regime. At low magnetic fields a resistance peak appears, which we ascribe to a size effect due to boundary scattering. Shubnikov-de Haas oscillations in fully encapsulated samples show all integer filling factors due to complete lifting of the spin and valley degeneracies.