"The long term storage of significant amounts of antihydrogen should soon settle the question of whether antimatter falls up or down."
One reason they would like to know if antimatter is repelled by gravity is that it could explain why the Universe is expanding at an accelerating rate.[1]
[1]: http://www.physorg.com/news/2011-04-antimatter-gravity-unive...
Would this mean that if I am "holding onto" a chunk of antimatter heaver than myself I will fall up into space?
But yeah, one theory is that if you hold one that's more massive than you are, its repulsion would overpower your attraction, and bang, zoom, straight to the moon!
10g of antimatter yields about 10^15 Joules - i.e. 1 PetaJoule, or the equivalent of a 2+ Megaton nuke.
If you were holding onto a chunk of antimatter large enough to hold onto you'd be missing half of London.
That's what nukes do too. Turns out that dumping absurd amounts of light (various parts of the spectrum, but certainly including visible) into the surrounding area absurdly fast tends to fuck stuff up pretty good.
By contrast, if you were holding a lump of antimatter contained by an electromagnetic field, a power failure would result is the antimatter escaping confinement and annihilating with your body, releasing an unimaginably large amount of energy nearly instantly. This is what you might call a "fail-deadly" system, because a failure results in a decidedly unsafe state.