CO2 is a gas so it is normally evenly distributed. if you had an eruption of gas from a volcano, then the mass of gas would be heavier than air and it would sink to the ground until it dissipated. A single molecule doesn't have enough mass to move by itself because it is constantly bouncing off other gas molecules.
You would get a slight tendency of heavier molecules staying near the surface. I believe that is the fundamental physics behind the historic temperature data from ice core samples. Heavier isotopes get to a higher altitude in the atmosphere when it is warmer because the molecules have more energy and diffuse them better. More of the heavier isotopes of oxygen and other compounds in the ice cores translates to higher temperatures but the ratios are very small.
CO2 could control climate because it is a green house gas. it is however hugely overshadowed by water and it is likely the effect isn't significant. There may be negative feedback mechanisms that reduce it but it should cause some warming because it absorbs thermal radiation. it warms when the ground below it is warm.
