At first the "Drink bottle" button seemed pretty ridiculous to me. Then I remembered that driving 200mph and having to negotiate a water bottle by hand would probably be impossible.
mostly road-going race cars: http://www.youtube.com/watch?v=JUhu13qp8Oc
f1 cars: http://www.youtube.com/watch?v=seget3zOj_8&feature=playe...
I'm an F1 fan but even that surprised me.
But maybe the best illustration of your point is obvious at a race. When the pace car is out -- and mind you, this is a top-of-the-line Mercedes sports coupe -- it's going around the track just as fast as it can, tires squealing and the whole works. And the parade of F1 cars is following as if it's a walk in the park, swerving left-and-right in an effort to keep their tires warm at such "slow" speeds.
Kinda like when you are waiting for a FPS game to load and you just make circles with your mouse pointer.
I would tend to believe that the swerving is mostly to feel the tyres and the car.
You're mostly correct. However, I believe the main reason for weaving is to prevent too much buildup (various debris from the track) getting on the tyres. Weaving helps to get some of the debris off the tyres.
Having said that, the F1 car is still substantially faster especially through a high speed corner like Eau Rouge.