Let us consider a 5 km tall air tank where cool air is at atmospheric pressure. At the bottom of the tank free path lengths of the atoms are 62nm. At the top of the tank free path lengths of the atoms are 124nm.
Now let us consider an atom that diffuses from the bottom to the top. The free path length of that atom increases by 62nm from 62nm to 124nm.
Let's say the average speed of the atom is 100m/s and it took million seconds to move from bottom to top.
So the atom traveled 100 million meters, which consists of, let's say 100 million meters / 62nm paths, that is 1.6*10^15 free paths.
Now let's consider an upwards directed free path, let's say the free path length increases during this free path by 62nm * (62nm / 5km) , that is by 7.7* 10^-19 meters.
Conversely during a downwards directed free path free path length shortens by 7.7* 10^-19 meters.
From the above we can conclude that upwards directed free paths are about 7.7* 10^-19 meters longer that downwards directed free paths.
So now let's say an atom moves 0.8*10^15 times a distance of 7.7 10^-19 meters, well that is only 0.000616 meters total distance. From that we can conclude that the million seconds time was much too short. It takes 8116883 times more time for an atom to bounce from the bottom to the top. That is 257384 years.
To answer the question: An atom tends to float upwards, because upwards directed free paths are very slightly longer than downwards directed free paths. (The atom floats upwards if its weigh is low enough or its speed is high enough)
Upwards directed free paths are longer than downwards directed free paths, because free path are longer at upper areas than lower areas.
And free paths are longer at upper areas, because gases are thinner at upper areas.
If a helium atom is released in the middle of a room, after a minute it will have moved downwards at probability 0.499999 and upwards at probability 0.500001.