With the rapid development and popularity of social networks, how to protect privacy in social networks has become a hot topic in the realm of data privacy. However, in most of existing anonymity technologies in recent years, the social network is abstracted into a simple graph. In fact, there are a lot of incremental changes of social networks in real life and a simple graph can not reflect incremental society network well, so abstracting the social network into the incremental sequences becomes more realistic. Meanwhile, in real life most of the network contains weight information, that is, a lot of social networks are weighted graphs. Compared with the simple graph, weighted graphs carry more information of the social network and will leak more privacy. In this paper, incremental dynamic social network is abstracted into a weighted graph incremental sequence. In order to anonymize weighted graph incremental sequence, we propose a weighted graph incremental sequence k-anonymous privacy protection model, and design a baseline anonymity algorithm (called WLKA) based on weight list and HVKA algorithm based on hypergraph, which prevents the attacks from node point labels and weight packages. Finally, through a lot of tests on real data sets, it proves that WLKA can guarantee the validity of the privacy protection on weighted graph incremental sequence. Compared with WLKA, HVKA is better to retain the original structure properties and improves the availability of weight information, but it also reduces the time cost of anonymous process.