The carb float probably needs to be adjusted, or the needle valve is leaking. It could leak if it has something partially stuck in it so it wont seat all the way, or could be worn down. When the rpms go up it uses more fuel than is leaking, so it runs better, when its idleing more fuel is getting fuel than it use, so the carb overflows making it run poor or die.
My 85 brat averages 34mpg per tank driving 110 miles per day, I would think a gen 1 would get slightly better.