In this paper, we consider the parametric H-infinity problems of weighted interval plants, A sufficient condition will be given on weighting function W(s) such that for any interval plant P(s, q, r) the maximal H-infinity norm of W(s)P(s, q, r) is achieved at one of the 16 so-called weighted Kharitonov plants. It is shown that for first-order and some high-order stable weighting functions, the extremality property is enjoyed generally by the maximal H-infinity norm of weighted interval plants.