To perform as successfully or be as influential as one has the ability or potential to do. A reference to weight classes in boxing. Their squad had been dominating the league in recent weeks, but they failed to punch their weight on Saturday night. There have been talks of reorganizing the way city councils are represented so that each region is better able to punch their weight when deciding budgetary issues. She may be new to the scene, but she's well able to punch her weight alongside industry veterans.