When you're using different air in tyres, you're not doing it to save weight. As itrpo has already calculated, you're only saving a couple of grams.
The reason you do it is related to how you want your tyre pressures and temperatures to change during a session.
You all know that the pressure you put in your tyre before you go out on track wont be the same as when you come in. The tyre heats up and therefore increases in pressure as per your high school physics Pressure=Temperature/Volume. The volume in your tyre is approximately the same, so as your tyre heats up, the pressure has to increase.
However, PV=T is not actually completely correct. The ideal gas law is really PV=NkT. That extra 'Nk' bit is dependant upon the type of gas you're using. Therefore the pressure of gases varies with temperature differently depending on the gas you use.
Therefore, you may find that using Nitrogen, for example, gives you a more predictable pressure change as the tyre heats up.
That's the science behind why you would use different air, it's to give you different effects on the pressure as the temperature changes.
Some order of magnitude calculations however show me that unless you're measuring your pressures to within half a psi, you're not going to be able to accurately measure the effects, so don't bother.
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