a box is sitting on the ground, and the ground does not increase nor decrease in elevation, nor does the surface go from rocky to muddy. it's just a regular surface that can be used to push boxes.
if you increase the acceleration of the box moving across the surface, does the force of gravity decrease? or is there a threshold that acceleration must surpass for the force of gravity to decrease and cause flight?
Nothing will happen. The force of gravity will be constant until you start getting into relativisitic velocities. I'm assuming a universe with nothing in it but an infinite massive plane and your box. The force of gravity will just be constant. You can push the box as fast as you want up to light speed of course, and its mass will increase along with this speed. This will increase the gravitational force between the box and the plane. There is no upward force. Maybe you're thinking about aerodynamic lift?
To sum up:
- The force of gravity does not depend on acceleration.
- The force of gravity does depend (only) on the objects' masses and the distance between them.
- The mass of an object depends on its velocity according to relativity (higher velocity => higher mass => more gravity). This effect is negligible at velocities much smaller than the speed of light.
- Given an atmosphere, additional forces such as lift and drag may araise, as a function of velocity, due to aerodynamics. Of these, lift counteracts the gravitational pull.
- If your "plane" is the surface of a planet (e.g. earth), it is not really a plane, but is spherical. In that case you need to take orbital constraints into account.