This is an explanation of the center of mass (or the centre of gravity) for animation. It also highlights new feature in our character rig to assist with animating around the centre of mass when a character is holding something. If this feature proves successful I'll implement it in the other two rigs.

There's another manual method for refining the center of mass when a character is holding a wand. Constrain a locator to it's center of gravity. Bake it's curves in world space. Duplicate the locator with the animation. Then constrain his wrist (with maintain offset) to both locators and delete (or mute) his original wrist animation curves. Now smooth out the curves of one of the locators taking out all the quick changes. The mix will be a blend of the exact animation and a more weighty smoother version at the center of gravity where the weight is. You can adjust the constraint weight between the two to get the best result.