Anti-gravitons... ;-)
Simply nulling the weight of an object is pointless. You'd still have problems turning corners with a million tonnes of mass and its associated inertia in your pocket!
And the Aircraft carrier might well become light enough to float in the air like a dirigible, but it would need massive air fans to move the mass needed to accelerate and manouevre.
Or you could connect it to trucks or horses on the ground and drag it along like an aerial barge...
Now, if you could null inertial mass, then we can go startrecking...