I'm with Rider, if you view it as a "classic" physics class problem, ie weightless ropes and pulleys (and hence no angular inertia for the pulleys, and no inert

I'm with Rider, if you view it as a "classic" physics class problem, ie weightless ropes and pulleys (and hence no angular inertia for the pulleys, and no inertia due to the ropes), and no friction, weight A would rise even without pulling the rope, weight B would remain static, and weight C would drop at the same rate that weight A would go up. If you pulled on the rope you could never make weight C go up faster than weight A until it hit the top and stopped moving. So the pulling bit is a red herring, as weight A would always hit the top before the other two, either pulling or holding it still. Assuming the weights are in kilograms you would have to let the rope go at a rate of 3.13 m/s (11.27 kph, 7 mph) to prevent weight A from rising.