  Heterostructures formed between two different van der Waals materials enable
interactions and functionalities absent in each component. In this work we show
that vicinity to an atomically thin WSe$_2$ sheet dramatically impacts the
energies of the symmetry-broken low Landau levels of bilayer graphene, possibly
due to screening. We present a systematic study of the magnetic field and
electrical displacement field dependences of the Landau level gaps at filling
factor $\nu$ = 1, 2, 3, and compare to BN encapsulated pristine bilayer
graphene. The exchange-dominated energy splitting between the N = 0 and 1
orbital wave functions is significantly enhanced, which leads to a modified
phase diagram at filling factor $\nu$ = 0 and larger energy gaps at $\nu$ = 1
and 3 in WSe$_2$/bilayer graphene heterostructures. The exchange-enhanced spin
gap at $\nu$ = 2, on the other hand, is reduced by approximately two-fold. Our
results demonstrate a possible way to engineer quantum Hall phenomena via van
der Waals heterostructures.
