To stay in the air we accelerate the unbalanced wheel during half a cycle and decelerate it during the other half. This creates momentum additionally to the (already present) vertical movement in the same or opposed direction.

The angular momentum applied to the unbalanced wheel either when slowing down or speeding up is always pushing the unbalanced wheel down (as a whole) Both acceleration and deceleration require opposed reaction forces in their opposed directions. The equally large response force is always pushing the the apparatus upwards.