Li and Zhou developed a method to compute elementary siphons and indicated that it may be extended to weighted resource allocation systems. The author shows a better way to find elementary siphons for weighted S3PR (systems of simple sequential processes with resources) or WS3PR via an example where there is no dependent siphon based on the approach by Li and Zhou. Yet, the author is able to locate one; thus, reducing the number of monitors required. Redefining the characteristic P-vector by weighting each component by that of a P-invariant, the author shows via a theorem and an example that an S3PR and its weighted S3PR have the same sets of elementary, dependent siphons and systems of equations of characteristic T-vectors. Applying their siphon-synthesis theory, the time to find elementary siphons for WS3PR is reduced from exponential to polynomial. The author also derives the controllability condition for a WS3PR and discuss how to extend to S3PGR2 (systems of simple sequential processes with general resources requirement).