CO2 is heavier than air (1.51 while oxygen is 1.1 and nitrogen is 0.97), however when combusted, it will initially rise until it's temperature gets closer to that of air (about 1000 feet), then it will tend to fall. CO2 is a reluctant defusser and mixer, so how does it get from 1000 to 10,000 feet - what lifts CO2 up?
...so how does it get from 1000 to 10,000 feet - what lifts CO2 up?
Hmm... how does it get to the mid-troposphere and higher?
Well, first, to understand that one may find some helpful information in comments below the question. Second, it always helps to review our own assumptions.
In the question, there's an implicit assumption that CO2 does not mix with the rest of the atmosphere at the molecular level. As it turns out, it does!
Also, the primary mixing mechanism in the troposphere takes place through eddy diffusion, not molecular diffusion, and that's an important distinction. Storms and jet streams, convection, and turbulence (from storms and clouds down to the nearly molecular size) all contribute to mixing.
As one goes higher in the atmosphere, the balance between the magnitude of eddy diffusion and molecular diffusion shifts. This happens above the tropopause.