Fb is not = W, the apparent weight.
Fb opposes the Weight, or mg.
So the apparent weight, W = mg - Fb
Imagine you're holding onto a rope suspended in the air, attached to the pulley.
The pulley has a friction to it, so that you won't drop nearly as fast. In fact, just hanging onto the pulley, you and the rope move very slowly downward.
This tension that the pulley has is kinda like the Bouyant force, in that it's pointing in the opposite direction of mg, and thus helps decrease your "apparent weight".