It might help in realizing that for a rope, tension is the same everywhere along it. Each time the rope pulls upwards, there's a force/tension applied in the upward direction. This upward force is countered by the weight of the object. Assuming you're pulling at constant velocity, which is the case most of the time, then the net force = 0N.

If Fnet = 0, then weight = Tension 1 + Tension 2 + Tension 3

Earlier I said these tensions are equal, so instead I should say that:

Weight = 3T (where T = tension in rope).