  Heterostructures of atomically-thin materials have attracted significant
interest owing to their ability to host novel electronic properties
fundamentally distinct from their constituent layers. In the case of graphene
on boron nitride, the closely-matched lattices yield a moir\'e superlattice
that modifies the graphene electron dispersion and opens gaps both at the
primary Dirac point (DP) and the moir\'e-induced secondary Dirac point (SDP) in
the valence band. While significant effort has focused on controlling the
superlattice period via the rotational stacking order, the role played by the
magnitude of the interlayer coupling has received comparatively little
attention. Here, we modify the interaction between graphene and boron nitride
by tuning their separation with hydrostatic pressure. We observe a dramatic
enhancement of the DP gap with increasing pressure, but little change in the
SDP gap. Our surprising results identify the critical role played by
atomic-scale structural deformations of the graphene lattice and reveal new
opportunities for band structure engineering in van der Waals heterostructures.
