Try selecting the summoning doll alone, and then click on a chest or piece of equipment on the ground a moderate distance away, and see if that will get it to move.
So even with everything removed from the doll the weight does not drop? That happened to me once selling everything a doll had, but simply handing him a small object and moving it in his inventory updated the weight he was carrying.
The pink spiral is a time penalty that prevents the doll from being used right away after summoning if it just died or ran out of bounds. If you move the mouse over the doll (and maybe the portrait) it should show a timer counting down the remaining penalty, IIRC. If you click on the doll statuette to unsummon it, you will not get the penalty if you resummon it right away.
