I present a simple scheme for the treatment of gravitational interactions on galactic scales. In anal- ogy with known mechanisms of quantum field theory, I assume ad hoc that gravitation is mediated by virtual exchange particles – gravitons – with very small but non-zero masses. The resulting den- sity and mass profiles are proportional to the mass of the gravitating body. The mass profile scales with the centripetal acceleration experienced by a test particle orbiting the central mass, but this comes at the cost of postulating a universal characteristic acceleration a0 ≈ 4.3 × 10−12msec−2 (or 8πa0 ≈ 1.1×10−10msec−2). The scheme predicts the asymptotic flattening of galactic rotation curves, the Tully-Fisher/Faber-Jackson relations, the mass discrepancy–acceleration relation of galaxies, the surface brightness–acceleration relation of galaxies, the kinematics of galaxy clusters, and “Renzo’s rule” correctly; additional (dark) mass components are not required. Given that it is based on various ad-hoc assumptions and given further limitations, the scheme I present is not yet a consistent theory of gravitation; rather, it is a “toy model” providing a convenient scaling law that simplifies the description of gravity on galactic scales.