80% of earth's atmosphere is nitrogen, I doubt there is a significants in weight saving. Some of my friends do fill their tires with nitrogen tho. When we go out (and try to drift), the back tires are pumped up to 50 psi or more. We think nitrogen behaves better than regular air in higher pressure and hotter conditions.
I think F1 uses nitrogen, a pure gas is a lot more predictible than a combination of gases in "regular air", epecially the condition is super hot and every 1/4 of psi can make a difference in a car's behavior.