The force pushing the gas away from the surface is the thermal movement of particles. Collisions between molecules are constantly exerting a pressure against surrounding molecules, although the net movement of molecules is overall zero from Brownian motion alone. The Earths gravity adds a downward component to the net velocity of particles in the gas, so that on average more fall down than up while the amount that move side to side is unaffected. This is why higher gas has a lower pressure than lower gas and why the air has horizontally same-pressure layers. As more particles fall down they add to the kinetic energy of lower layers, increasing the temperature below (in addition to the suns rays). This of course exerts a pressure upward. The current density profile of the atmosphere is the balance between heat pushing gas apart and gravity pulling it down.
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