Graphene is impermeable to gases, but introducing subnanometer pores can allow for selective gas separation. Because graphene is only one atom thick, tunneling can play an important role, especially for low-mass gases such as helium, and this has been proposed as a means of separating He-3 from He-4. In this paper, we consider the possibility of utilizing resonant tunneling of helium isotopes through nanoporous graphene bilayers. Using a model potential fit to previously reported DFT potential energy surfaces, we calculate the thermal rate constant as a function of interlayer separation using a recently described time-independent method for arbitrary multibarrier potentials. Resonant transmission allows for the total flux rate of He-3 to remain the same as the best-known single-barrier pores but doubles the selectivity with respect to He-4 when the optimal interlayer spacing of 4.6 angstrom is used. The high flux rate and selectivity are robust against variations of the interlayer spacing and asymmetries in the potential that may occur in experiment.