  Single layer $\alpha$-ruthenium trichloride ($\rm\alpha-RuCl_3$) has been
proposed as a potential quantum spin liquid. Graphene/$\rm RuCl_3$
heterobilayers have been extensively studied with a focus on the large
interlayer electron transfer that dopes both materials. Here we examine the
interplay between the competing magnetic state of $\rm RuCl_3$ layer and
graphene electronic properties. We perform self-consistent Hartree-Fock
calculations on a Hubbard-Kanamori model of the $4d^5$ $t_{2g}$ electrons of
$\rm\alpha-RuCl_3$ and confirm that out-of-plane ferromagnetic and zigzag
antiferromagnetic states are energetically competitive. We show that the
influence of hybridization between graphene and $\rm\alpha-RuCl_3$ bands is
strongly sensitive to the magnetic configuration of $\rm RuCl_3$ and the
relative orientations of the two layers. We argue that strong hybridization
leads to graphene magneto-resistance and that it may tilt the balance between
closely competing magnetic states. Our analysis can be applied to any van der
Waals heterobilayer system with weak interlayer hybridization and allows for
arbitrary lattice constant mismatch and relative orientation.
