From your comments it seems that effectively you are asking about "why do gases mix so easily?"
If a system such as a mixture of gases is kept under constant temperature in a constant volume, the equilibrium state corresponds to the minimum of Helmholtz free energy:
$$A = U - TS$$
As you see, for $A$ to reach the minimum either the energy $U$ should decrease or the entropy $S$ should increase (or both in reality).
Minimizing energy. Most of the energy of common gases at normal conditions comes from their kinetic energy defined by the temperature. Energy due to intermolecular potential is negligible. So the only possibility to lower the energy is to lower the gravitational energy. In essence it would require the mixture to perfectly separate --- heavy gases at the bottom, light gases up.
Maximizing entropy Maximum entropy for the system in hand (under specified conditions) would imply perfect mixture, the state of most disorder. That's actually what drives the diffusion.
So as you see, the equilibrium state is a compromise between low energy and high entropy. For gases the entropy wins, because there isn't much energy difference between a mixture and a separated state (apart from gravity, which is still small).
As for your example with oil and water the situation is opposite. Unlike gases considerable amount of energy in liquids comes from intermolecular forces. Thus there is a huge differences in energy of interaction water-water or water-oil, so it is more preferable do separate to considerably minimize the energy.