The matrix-like structure of the Weight Function (WF) for determining the Stress Intensity Factors (SIFs) in a nonsymmetric plane body is obtained from the general properties of the elastic field. General asymptotic and symmetric properties of the WF are discussed. By extending a previously proposed methodology, an analytical approximate WF is determined for an edge crack in a semiplane within the range of inclination. (-75 degrees, + 75 degrees). Finite Element evaluations considering the minimum number of loading conditions were performed to this purpose. The accuracy of the SIFs obtained by the WF is found in the order of a few tenths of percent. The solution of a typical problem illustrates the practical usefulness of the WF.