Nice paper: Constraints on possible "antigravity" of antimatter Answered
A new preprint on arXiv does an excellent job of deriving strong constraints on the possible "antigravity" (gravitational repulsion) of antimatter, based on very precise experimental data and a minimum of theoretical assumptions. Karshenboim goes through several complex and detailed analyses to set tight limits on antigravity effects.
The argument I like best goes as follows: if antimatter feels a gravitational repulsion relative to matter, then "pure neutral" bodies, like positronium (bound states of e+ and e-) or photons (which are their own antiparticles) should feel no gravity at all. That trivially contradicts the gravitational deflection of light, and therefore can't be true.