Theil's measure of information has found many applications in economics and statistics, pattern recognition, decision theory, and prediction theory. The idea of weighted information improvement (WII) as a measure has been defined recently by authors. This idea has further been extended in the present communication to two, and to subsequent, finite revisions. The weighted additivity under the sum property generates the generalized functional equation whose solutions characterize the weighted information improvement due to two, and to subsequent, finite revisions. Some particular cases are also discussed.