B. Because the upward pull of rope A on the weight and the downward pull of the weight on rope A are a pair of interaction forces, option B is wrong;
C, because the weight is in a state of balance, and the object is only subjected to downward gravity and upward pull of the rope A on the weight, so the upward pull of the rope A on the weight and the gravity of the weight are a pair of balancing forces, so option C is correct;
D, because the downward pull of heavy objects on the rope A and the downward pull of people on the rope do not act on an object, which is not a balancing force, option D is wrong.
So choose C.