As far as i understand it, the lower the bats centre of mass, the further the centre of mass is from your top hand around which the bat pivots. so to make the bat rotate around the top hand by the same amount, you need to put more force on the handle with your lower hand. A counter-weight has the effect of adding to this force from the bottom hand, and causing the bat to pivot more about the top hand. this means you can have more weight or a lower centre of mass without making the pickup heavier and without increaing fatigue.
In your pickup though, most people also raise the entire bat up a bit rather than solely rotating it around the top hand. The greater the weight of the bat, the more force you need in your arms to pull the bat up and so the more tiring this action is. In this respect then, adding a counterweight will only make the bat heavier and so make pickup more tiring.