You're mistaken. For trips that originate or terminate in the United States, the marketing carrier of the first segment sets the policy used for the entire trip. It's a US DOT regulation, and it's designed to protect people from sticker shock at check-in time when bags that were free for their first flight suddenly cost an arm and a leg.

Carriers (United included) are well aware of the regulation. In fact, if you view your receipt, there should be a phrase on it like this "In compliance with U.S. Department of Transportation regulations, checked baggage policies for your entire itinerary are determined by <Insert carrier here>." What UA isn't always great about is getting its calculator to return the right value; however, if OP looks at a receipt, this phrase should be printed, and based upon the information provided, it would say "Copa Airlines."