Why would a bad head gasket cause the coolant reservoir to fill up?

First have someone run a cooling system pressure test. Follow this procedure. Install the pressure tester. Pump it up to 5 psi and see if it holds that pressure. It might. Then start the engine and watch the pressure gauge. Goose the throttle. Does the gauge jump? If so, you have a blown head gasket…Many big shops have a hydrocarbon sniffer that can tell FOR SURE.