Weighted networks can give more detailed description of interaction between agents of corresponding systems. Link weight also provides another way to improve the properties and functions of networks. Based on the concept of network efficiency in binary networks, in this paper, the efficiency of weighted networks with similarity or dissimilarity weight is defined. The effect of weight distribution on the network efficiency are investigated. From the initial regular network with homogeneous link weights, a method is introduced to randomize the weight distribution over the links. The results demonstrate that the random redistribution of link weight can improve the network efficiency. Moreover, exponential distribution of link weight shows more significant improvement compared with the other common distributions, such as uniform, Poisson, Gauss, and power law distributions. Meanwhile, it is also found that the total weight of the corresponding minimum spanning tree is reduced with the randomization of link weight. That means the cost of transportation is decreased with the increase of link weight heterogeneity. All these results can help us get deeper understanding about the effect of link weight on the property and function of networks.