According to Archimedes' principle, what determines the magnitude of the upward buoyant force acting on an object floating or moving through a gas?

The weight of the gas displaced by the object.

Explanation

Archimedes' principle applies uniformly to all fluids, including both liquids and gases. The upward buoyant force exerted on any submerged or floating object is always exactly equal to the weight of the fluid (gas) that the object's volume pushes aside.