https://pmc.ncbi.nlm.nih.gov/articles/PMC10533407/
The interesting idea behind it is basically that for antimatter a potential wall, imagine a step function which is 0 for negative and 1 for positive and a wave that hits the wall from the negative to the positives, in theory it cannot propagate in the wall, turns out that one solution can propagate in that wall and that's antimatter: It basically sees the potential as inverted.
So since people were thinking about that they started considering that if it happens for EM interaction it could be the case for gravitation, that lead to wonder if the antimatter had different properties in that department.
From a pure theory point of view the mass of the particles and anti particles should be identical but they might have "fallen up" instead of falling down.
Note that if there are significant differences this would be extremely interesting but I am not deep enough into exotic theories that take into account those exotic cases to make more statements about the matter.
Which may have been true in a world where gravity was a charge or like the other forces. But it isn't. Everything with mass has mass. There is no detection of any sort of anti-mass, no matter the exotic possibilities such a thing would enable.
I needed to know how much antimatter weighed and this article seemed helpful (though I am poorly placed to know if it’s correct).
https://gizmodo.com/how-much-does-antimatter-weigh-492195828