1 Iki Piki: So, setting aside cannibalism and bringing some sensibility back into this discussion, what can we do to fix the engine, Spanners?
2 Spanners: We need to shift a three-tonne block of metal and antimatter.
3 Serron: Antimatter’s like negative matter, right? Does it reduce the weight?
3 Spanners: No, it doesn’t work that way.
4 Serron: Oh. Well, if it had been a bit less than three tonnes I would have been able to help.
4 Serron: Anyone seen the teriyaki sauce?

Although theoretically we believe that antimatter particles have the same mass as their matter counterparts, and are affected in the same way by gravity, we have never experimentally verified this.

The reason is that we've never managed to assemble enough antimatter into one place to do any experiments on it related to mass gravity. Importantly, although we have theoretical reasons to think that gravity produced by matter attracts antimatter in exactly the same way as matter, we don't know for sure that antimatter isn't in fact repelled by normal matter, or that if it is attracted that the magnitude of the attraction is the same as that for matter.

The problem is that almost all of the antimatter we've generated and experimented with is electrically charged particles, and the electromagnetic force vastly overwhelms the force of gravity at small scales. In 2010, the Antiproton Decelerator at CERN began to produce stable antihydrogen atoms, which are electrically neutral (an antiproton surrounded by a positron, or anti-electron). In principle we can do mass-related experiments on these anti-hydrogen atoms, but unfortunately we can only produce a small number of them at a time.

In 2012, CERN performed the first experiments attempting to measure the gravitational interaction on antihydrogen atoms, by subjecting them to free-fall in Earth's gravity field. They measured that the gravitational interaction was consistent with antihydrogen having the same mass as hydrogen, to within an experimental uncertainty of ±7500%.^[1]

That's pretty uncertain, and it leaves the door wide open for the antihydrogen to actually be repelled by the Earth's gravity. Later experiments in 2013 reduced the uncertainty to ±100%. Consistent with either normal mass... or zero mass... or anywhere from that to double the mass of hydrogen.

These are pretty tough experiments!

Eddy W. points out:

I know the gravitational influence has not been measured, but we've known the inertial mass agrees with that of normal matter for about as long as we've known about antimatter. Specifically, beta-minus-rays and beta-plus curve in a magnetic field in opposite directions but to the same degree; and, similarly, all the accelerators that have been accumulating that anti-hydrogen have relied on the charge-to-inertial-mass ratio being the same as for normal matter in order to manage the antimatter. So the "same mass as their matter counterparts" of the initial statement has been verified, it's only the "affected in the same way by gravity" part that we have never verified. The real question of interest, that stands still unverified, is thus whether their gravitational and inertial masses coincide, as we expect on theoretical grounds, or whether Einstein's principle of equivalence of inertial and gravitational mass breaks down for them.

[1] Amole, C.; Ashkezari, M. D.; Baquero-Ruiz, M.; Bertsche, W.; Butler, E.; et al. (2013). "Description and first application of a new technique to measure the gravitational mass of antihydrogen". Nature Communications. 4: 1785. https://doi.org/10.1038%2Fncomms2787.