One day, I decided to calculate the density of air, so I searched for the individual densities of the 3 main elements that forms breathable air. I found the following data, at $\pu{0^\circ C}$ and $\pu{100 kPa}$:

\begin{array}{lrS} \text{Component} &\% &\rho,\,\pu{g cm-3}\\ \hline \text{Nitrogen} &78 &0.001251 \\ \text{Oxygen} &21 &0.00142897 \\ \text{Argon} &1 &0.001784 \end{array}

I'm calculating the density of $\pu{1 cm3}$ of air. Individual masses in $\pu{1 cm3}$ of air:

\begin{align} &\text{Oxygen} &\pu{0.0003000837 g}\\ &\text{Nitrogen} &\pu{0.00097578 g} \\ &\text{Argon} &\pu{0.000001784 g} \\ \end{align}

The final density is equal to $\pu{0.0012937037 g cm-3}$

Then I realized that the density of ozone should be lighter due to the ozone layer to be able to exist, otherwise, the ozone gas, as it is fairly more dense than air, would pass directly through the atmosphere. The problem is that the density of ozone gas at the same conditions (STP), have a density of $\pu{0.00214 g cm-3}$, which is $65.41654785\%$ heavier than air.

With the context explained, my question is: if is really a ozone layer up there in the atmosphere, how it is there, being heavier than the base gas mix that is below it?