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Fuzzy rule interpolation techniques have been used to handle the problems of sparse fuzzy rule bases in sparse fuzzy rule-based systems. In the existing fuzzy rule interpolation methods, there are many variables in the antecedents of fuzzy rules, where the variables in the antecedents of fuzzy rules have the same weight. If we can handle fuzzy rule interpolation with weighted antecedent variables, then there is room for more flexibility. In this paper, we present a new method for multiple fuzzy rules interpolation with weighted antecedent variables. The proposed method not only can handle fuzzy rule interpolation with polygonal membership functions, but also can preserve the convexity of fuzzy interpolative reasoning results. The fuzzy interpolative reasoning results of the proposed method also satisfy the logically consistency with respect to the ratios of fuzziness. The experimental result shows that the proposed method can generate reasonable fuzzy interpolative reasoning results for sparse fuzzy rule-based systems with weighted antecedent variables. The proposed method provides us a useful way for fuzzy rule interpolation in sparse fuzzy rule-based systems with weighted antecedent variables.