[matthewdenny]

While the weight of the ball doesn't change, the location of the downward vector relative to the pivot does. For example when the ball is directly below the pivot of the arm gravity is pulling down on the ball, and if you look at the line of this vector it passes through the pivot point, effectively making the lever arm 0, and the torque also 0.

Note: I'm not saying that I'm sure this is right, but that was the logic.