I'm interested in antimatter too. There should be a lot of antimatter out there, but we can't seem to find it. It's possible that antimatter does interact gravitationally at a smaller magnitude with matter and/or other antimatter. As far as I know, we haven't even experimentally confirmed whether antimatter has the same sign for gravitational effects as regular matter (ie whether it's repulsive or attractive), but it seems very likely that it's the same as regular matter. The magnitude could be different though.
Keep an eye on ALPHA at CERN. It is designed to answer this exact question by producing anti-hydrogen atoms. https://home.cern/news/news/physics/alpha-collaboration-cern.... Their initial results a few years back were consistent with matter and antimatter acting the same under gravity, but their error bars were large enough to warrant a more precise measurement, which they're up to now.
