Why does atmospheric pressure change with altitude?

Pressure at the top of a mountain...

Atmospheric pressure reduces with altitude for two reasons, both of which are related to gravity.

1. The gravitational attraction* between the earth and air molecules is greater for those molecules nearer to earth than those further away — they have more weight — dragging them closer together and increasing the pressure (force per unit area) between them.
2. Molecules further away from the earth have less weight (because gravitational attraction is less) but they are also ‘standing’ on the molecules below them, causing compression. Those lower down have to support more molecules above them and are further compressed (pressurised) in the process.

* Strictly speaking, it is the gravitational force minus the effect of the Earth's spin (an effect that is greatest at the equator).