Recently, massive digital records have made it possible to analyze an enormous amount of data in various research fields, such as social network analysis and systems biology. We investigate weighted relatedness networks by extracting information on the World Wide Web. Using famous search engines such as Google, we quantify the relatedness between two objects as the number of webpages including both of their names and construct weighted relatedness networks. We take some representative examples in relatedness networks among people, measure the distributions of quantities of interest in weighted network analysis, and present a class of measure called Renyi disparity, which characterizes the homogeneity of weight distribution for an individual node. The concept of maximum relatedness subnetwork, which captures the most essential relation for each individual, is also introduced. As an example, we analyze the members of the 109th United States Senate and demonstrate that the methods of construction and analysis are applicable to various other weighted networks.