We use a van der Waals pickup technique to fabricate different heterostructures containing WSe2(WS2) and graphene. The heterostructures were structured by plasma etching, contacted by one-dimensional edge contacts, and a top gate was deposited. For graphene/WSe2/SiO2 samples we observe mobilities of similar to 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 WSe2(WS2) and hexagonal boron nitride show a much higher mobility of up to similar to 120 000 cm(2) V-1 s(-1). However, in these samples noWAL 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.