You'd get more weight savings by trimming the elastic on your underwear.

It wouldn't affect the spring "rate" of the tire. Pressure would regulate the spring "rate" of the tire, regardless of what that pressure is caused by.

No...not the ideal gas law, now he has to look something else up!

Whazzup, what are you trying to figure out? The air in the tire, for weight saving purposes, is pointless.

Also, helium is such a small atom, it would leak out over time, causing a pressure loss. Pressurizing it into tires would probably only make it more apparent. That's why helium baloons deflate, the helium actually escapes through the rubber.