Recent experiments suggest quantum interference effects in the Coulomb drag of double-layer graphene systems. By accounting for correlated interlayer impurity scattering under a weak magnetic field, our theoretical results reveal drag resistivities resembling those in weak (anti-)localization. It is established that the quantum interference effect is most significant when the chemical potentials match. The theory clarifies the roles of intra- and interlayer Berry phases in Coulomb drag in double-layer graphene systems and helps delineate the intra- and intervalley contributions. These insights are valuable for designing graphene-based electronic devices exploiting quantum effects.