The described pulley setup will simply accelerate until it reaches one limit or the other depending on the balance of weights. In order to have the position vary with the load, you need a position-varying force, such as

• A spring.
• A rotating off-center mass, as in a balance scale. (This is nonlinear for large angles.)
• An asymmetric pulley, i.e. a cam (in the shape of an Archimedean spiral).
• A tall object (of constant cross-section) entering a pool of water.