Examples of when it is not advantageous to be lightweight

Aside from the obvious loss of friction due to a decreased normal force affecting pushing ability, I cannot think of any specific examples in FRC history when it has been disadvantageous to be as light as possible. Is there anything I am missing, and if so, could you cite a specific match that shows this weakness due to weight? Also, is there a limit with weight where, like adding motors, you reach a point where it becomes less and less advantageous to become lighter?

I appreciate all input.