What about anti-matter? Does that have "anti-gravity?"
We've made plenty of anti-matter, surely we'd have noticed by now.
It turns out to be a little less than obvious. We load anti-protons in an accelerator and store them in orbit for hours. They don't behave differently (except for the sign of their charge) than the protons do. But they're confined in orbit by strong magnetic fields, and if they start to fall down (or fall up) the field bends their paths back to where they belong. Protons don't fall out. Neither do anti-protons.
We get anti-electrons from nuclear decay all the time. They come out of the nucleus with energies high enough to give them speeds that are an appreciable fraction of the speed of light, and then they start playing pachinko with other electrons along the way. The effects of gravity get lost in the noise.
Trying to hold onto anti-matter is a bit fraught. It won't sit politely in your test tube.
So the ALPHA collaboration has tried to make a little magnetic bottle to hold atoms of anti-hydrogen. When they turn off the magnetic field, the atoms fly around, hit the sides of the detector, and start annihilating with ordinary matter. If more of them hit the top than the bottom, does that mean they feel anti-gravity?
The devil is in the details. The anti-atoms aren't perfectly cold, so they have a distribution of velocities that sends them in all directions. The effect might be small. Also, the field doesn't turn off instantly, as Nature explains. That might bias the directions they fly in. The fast atoms escape quickly, and the slow ones--the ones you might expect 9.8m/sec^2 to matter for--trail out later.
The collaboration is building a better detector, so they can cool the anti-atoms further, and make better estimates. Right now their limits are not very good--but it says something about the difficulty of studying antimatter when you learn that their limits are the best direct limits so far. "If an antihydrogen atom falls downward, its gravitational mass is no more than 110 times greater than its inertial mass. If it falls upward, its gravitational mass is at most 65 times greater." That's the problem when you've only got 23 events to play with.