I have some doubts that such a craft would be manipulating gravity. If gravity could be manipulated then I would expect that a laboratory would have been able to discover some signs of it by now. There have been billions of dollars spent on trying to find the quantum or fundamental source of gravity, with researchers trying everything any anything, to little avail. Decades and decades of fundamental research has left the greatest minds in physics stumped. They have basically given up on it by now. If a scientist wanted to create something that did what a UFO did it would be easier to explore known existing phenomena.
A fly can make zig-zaggs through the air on a dime, unlike a plane.
A child who lets go of their balloon into the atmosphere can make vertical maneuvers that are somewhat difficult for a plane for perform.
I bet a plane can't distribute its weight like this:
In fact, by manipulating the angular momentum of a very heavy spinning wheel, its weight can be more easily manipulated. This guy is swinging around a heavy metal object above his head that he can't lift at all when not spinning.