How does the concept of hydrostatic equilibrium explain the variation of atmospheric pressure with altitude?

Hydrostatic equilibrium means that the weight of the air above a given level is exactly balanced by the pressure pushing upward from below, so the atmosphere stays steady. Because each layer of air has mass, the pressure at a lower level must support the weight of all the layers above it, which makes the pressure larger near the ground. As you go higher, there is less air above you to support, so the pressure drops; the rate of drop is governed by the balance of weight and pressure gradient. For example, at 1 km altitude the pressure is about 80 % of the pressure at sea level, showing a clear decrease with height. Thus, hydrostatic equilibrium explains why atmospheric pressure steadily falls as altitude increases.