If the weight is moving, even slightly, that is a good sign. That's usually an early indication that it is about to break free. Use the advice given above plus grab the weight with a large pair of Channelocks and twist in both directions.
They get jammed up with carbon. Sometimes they will free up with the carb and intake installed, sometimes not. If the latter, remove the carb and the intake to get at the inside of the valve. Scrape away as much carbon from the pivot points as you can with a small screwdriver, then hit it with Kroil from the inside and repeat the tapping/twisting procedure described above.
I have had them take over a week to break loose with spraying and tapping a few times a day. Persistence pays off. Usually, you'll first feel a little side to side give when you tap on the shaft, then the weight will start to wiggle. That's an indication that you are in the home stretch.
Good luck,
Matt