[8695Beaters]

You are half right. Low profile tires help handling because the sidewall doesn't flex as much as on a thicker tire. But that doesn't mean that it's always a good thing. Look at F1 tires: they are about 3 or 4 inches thick in profile, but these cars pull 3gs of cornering force on almost every corner they hit. What makes more of a difference in grip is tread compund and tread design. Larger tread blocks don't deform and add grip, but are very loud for street use. Also, a soft compund tire has much more grip than a hard tire, but also wears out very quickly.

As for weight, think about it like this: what's heavier, metal, or air and rubber? In most cases, the tire is lighter than the wheel and by adding wheel, you are increasing the rotational weight on the wheel/tire. If you took your regular and spare tires, and tried giving them the same push, the spare tire would take off a lot faster and go farther. If your friend tried to stop them, he would have a harder time stopping the full tire over the spare. The same thing applies to your car. Weight is bad on any level for performance, but on wheels and tires, one pound of weight is equal to about 2 pounds of chassis weight.