How does density affect our atmosphere

Warm air is less dense than cooler air. Air density varies with the relative humidity (amount of water vapor molecules in the air) along with temperature ... Dry air is composed mostly of Nitrogen (N) molecules since Earth's atmosphere is 78% Nitrogen and 21% Oxygen.

In the atmosphere we see significant thermal disturbances that change density of gases and add water vapor, a low density gas. Gases tend to redistribute because of their varying densities. so we will not find deep layers of one gas above deep layers of another gas. We do have Brownian movement that cause accumulation, but the nature of a gas overrules any tendency to completely stratify based on density.