The problem is that your heated grips are close to maxing out the 10 amp circuit for the acessory plug. You should never install a larger fuse in place of whats supposed to be there, as the factory fuse is sized for the wire installed on the bike. When you put in a large fuse, the fuse will never blow, but now the wire will burn off somewhere in the harness.
Run the wiring direct to the battery. If its 14 gauge, a 15 amp fuse will be correct on that circuit. if the wire is smaller (should be stamped in tiny letters on the wires jacket-or the instructions for the heated grips should tell you) google american wire gauge to see what the amp capacity of that size wire will handle.
The electrical system on the bike should keep up with your load with a good battery and a proper working stator.