Information entropy has been proved to be an effective tool to quantify the structural importance of complex networks. In a previous work [Xu et al. Physica A, 456 294 (2016)], we measure the contribution of a path in link prediction with information entropy. In this paper, we further quantify the contribution of a path with both path entropy and path weight, and propose a weighted prediction index based on the contributions of paths, namely weighted path entropy (WPE), to improve the prediction accuracy in weighted networks. Empirical experiments on six weighted real-world networks show that WPE achieves higher prediction accuracy than three other typical weighted indices.