Assumptions:
pulleys: idealized, massless, frictionless
rope: idealized, massless, doesn't stretch
weights: resting on ground.
As tension is applied to the rope, Weight A will be lifted first, until it is lifted to the ceiling. Then Weight B, and finally Weight A.It helps to visualize Weight A as being massless. In that case, there would just be extra slack in the rope, and B&C would not move until the slack was taken in.