How are the effects of antimatter on gravity different than regular matter?
They aren't. The formulas for general relativity doesn't care if something is matter or antimatter or not matter at all, just mass.
While the answer to the original question is correct, the assertion "just mass" is not. In GR, gravity couples ti energy, momentum and stress.
Isn't the correct answer to the question "we think that matter and anti-matter behave the same with respect to gravity, be we do not know for certain"? Part of the work of the ALPHA team at CERN is to probe anti-matter gravity http://dx.doi.org/10.1038/ncomms2787
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