  Weak measurements done on a subsystem of a bipartite system having both
classical and nonClassical correlations between its components can potentially
reveal information about the other subsystem with minimal disturbance to the
overall state. We use weak quantum discord and the fidelity between the initial
bipartite state and the state after measurement to construct a cost function
that accounts for both the amount of information revealed about the other
system as well as the disturbance to the overall state. We investigate the
behaviour of the cost function for families of two qubit states and show that
there is an optimal choice that can be made for the strength of the weak
measurement.
