I present a simple scheme for the treatment of gravitational interactions on galactic scales. In analogy 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 scheme predicts the asymptotic flattening of galactic rotation curves, the Tully-Fisher/Faber-Jackson relations, the mass discrepancy-acceleration relation of galaxies, and the surface brightness-acceleration relation of galaxies correctly; additional (dark) mass components are not required. The well-established empirical scaling laws of Modified Newtonian Dynamics follow naturally from the model. The scheme I present is not 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.