I am under the understanding that a toy top will weigh less when it is spinning. The Russians made a spinning type transport back in the 70s to lessen its payload over the tundra. Is this an effective way to beat gravity?
A top can offer stability like in a gyroscope, but it does not in any way reduce the mass of an object.
Some applications of a gyroscope are useful for transport, however. The popular Segway scooters use them to measure how far/fast it is tilting forward or backward and drives the wheels to compensate.. Similarly, motorcycles take advantage of the gyroscopic motion of their wheels to stay upright. Over the tundra, I could conceive of a gyroscope being used to keep a sled tilted up so that it is heavier on the backside and thus doesn't get caught toe up in the snow, but it would not reduce the mass at all. On the contrary, the mass of the gyroscopic device is just more to haul around.
To a certain extent yes, if you take aerodynamics into account. Specially made top can deflect air to provide a lift force. Exaggerated example is a helicopter. A better example though is Frisbee.
But it's not because the mass reduced or something is done to gravity, it's just a force exerted by surrounding air.
By the way, George, provide a reference to that Russian transport so we could see what's the matter with it.