[Neilk]

Originally Posted by Aragorn

The simple answer for the larger sidewall is rules. The F1 rules regulate the maximum size of the wheel (13-inches I believe.)

Modern F1 tires (tyres for our UK friends) act like a suspension component.

All F1 suspensions are stiff:

Formula 1® - The Official F1® Website

This allows the tire to act as a part of the spring rate and grip the road better:

Formula 1® - The Official F1® Website

Low profile tyres

I also read somewhere that it is a way to limit brake sizes, but not sure if that is really true.