We consider the scenario of excitons in a semiconductor bilayer that are strongly coupled to cavity photons, leading to the formation of dipolar exciton polaritons (dipolaritons). Using a realistic pseudopotential for the dipolar interactions, we exactly determine the scattering between dipolaritons, accounting for the hybridization between interlayer and intralayer excitons. We show that the light-matter coupling enhances the interactions between dipolaritons by forcing excitons to scatter at energies that would otherwise be forbidden in ordinary exciton-exciton collisions. Furthermore, we show that this light enhancement is sensitive to the dipole moment and is larger for long-range dipolar interactions than for short-range intralayer interactions. Our results reveal the role of dark exciton states in dipolariton interactions as well as the optimal bilayer properties for achieving strong interactions, which are crucial for quantum photonic applications.