Many realistic mobile social networks can be characterized by evolving bipartite graphs [1], [2], in which dynamically added elements are divided into two entities and connected by links between these two entities, such as users and items in recommendation networks, followees and followers in Twitter networks, authors and scientific topics in scholarly networks, etc. However, given the fact that connections between two entities are often weighted, how to mathematically model such weighted evolving bipartite relationships, along with quantitative characterizations, remains unexplored. Motivated by this, we develop a novel Evolving Bipartite Model (EBM), which, based on empirically validated power-law distribution on multiple realistic mobile social networks, discloses that the distribution of total weights of incoming and outgoing edges in networks is determined by the weighting scale and bounded by certain ceilings and floors. Based on these theoretical results, for evolving bipartite networks whose degree follows power-law distribution, their overall weights of vertices can be predicted by EBM. To illustrate, in recommendation networks, the evaluation of items, i.e., total rating scores, can be estimated through the given bounds; in Twitter social networks, the influence of users can be roughly measured; in scholarly networks