Does Antimatter Fall Up?

There has been some controversy about this question. An experiment at CERN is running a test to see if anti-Hydrogen falls differently in a gravitational field than regular Hydrogen. This experiment would use antimatter directly.

However, earlier gravity experiments to test the Weak Equivalence Principle claim to have already excluded this possibility. I go through their arguments here.

Image is the row of trees outside of Wilson Hall at Fermilab, taken from the Fermilab photo archives.