In wireless sensor networks, a weighted aggregation is an important method for the users to obtain the information when monitoring the environment. This method enforces the objectivity of the aggregation result by assigning different weights to different nodes or sensed data. On the other hand, the WSNs are both energy constraint and unstable, so it is better to do the approximate data aggregation if one can ensure the error-bound is tolerable for the users. A group-based sampling algorithm for approximate weighted aggregation is proposed. The theoretical analysis demonstrates that the proposed algorithm can reach arbitrary precision. Furthermore, the proposed algorithm is scalable, and it can adapt to large-scale dynamic sensor networks, and support the modification of the precision during the processing of a query. Experimental results show the correctness of the proposed algorithm and demonstrates the high performance of the proposed algorithm by comparing it with previous algorithms.