  We extend the two particle theory of disordered systems within the coherent
potential approximation CPA to obtain weighted contributions to averaged two
particle resolvents which arise from separate alloy components. Starting from
first principles in a model of diagonal disorder and the single site
approximation for a binary substitutional alloy $A_cB_{1-c}$ we extend the
approach of a fundamental paper by Velick{\'y} to evaluate various weighted
forms of a general class of two particle Green's functions. Applications in a
wide range of linear response theory are discussed in detail as well as the
behavior of the weighted functions in a strong disorder limit. To exemplify our
analytic calculations the optical absorption in a disordered model- alloy is
studied numerically.
