  We extend the idea of weak measurements to the general case, provide a
complete treatment and obtain results for both the regime when the pre-selected
and post-selected states (PPS) are almost orthogonal and the regime when they
are exactly orthogonal. We surprisingly find that for a fixed interaction
strength, there may exist a maximum signal amplification and a corresponding
optimum overlap of PPS to achieve it. For weak measurements in the orthogonal
regime, we find interesting quantities that play the same role that weak values
play in the non-orthogonal regime.
