Ozone is a gas heavier than air. Why does ozone layer not settle down near the earth?

In stratosphere, the formation of O3 goes on continuously but O3 is also decomposed by UV-radiation between 240nm to 360nm.
O3+H2(240-360nm)O2+O
The O-atom reacts will sand O3 molecule
O3+O2O2
Net reaction 2O33O2
Thus, the reaction form a delicate balance in which the rate of O3 decomposition matches the rate of O3 formation is a dynamic equilibrium exists and maintains a constant concentration of O3.