Adds, but not equally.
Take a cylindrical vessel of water. Drop a stone in it.
Water level will rise due to the volume displaced by stone.
The pressure of the stone on the tiny contact points to the bottom will be the weight of the stone minus the weight of water displaced by the stone.
The pressure of the water on the bottom is the weight of the water actually in the vessel plus the weight of the water displaced by the stone.
Ditto about Earth atmosphere.
Reenter a shuttle into atmosphere so that it is no longer supported by centrifugal force but by aerodynamic force, and the pressure of air will be weight of atmosphere plus weight of shuttle.
Land the shuttle, and the pressure of air will be weight of atmosphere plus weight of air displaced by shuttle.