Hmmmm. Did someone get busted for being underweight?
I used to run my oval cars super light (3-4oz under) at tracks that didn't weigh. Big advantage.
The F1 teams are spending zillions of dollars to make lighter fuel. Why? Because it's an advantage. Those guys are nuts.
A lighter RACE car will be more fragile, because you don't want to lose the existing rigitity of the chassis system. You could make a car out of nice flexible nylon/polyethylene that wouldn't break and it would be light, but it would be slow.
Why not run as light as possible? Because it is an advantage, period. The only racing that I can think of at the moment that doesn't have a minimum weight limit is gravity type racing (pinewood/soapbox derby, etc.). And they have max limits.
There needs to be rules, period. Keeps the rich guys honest.