The current data explosion poses great challenges to the approximate aggregation with an efficiency and accuracy. To address this problem, we propose a novel approach to calculate the aggregation answers with a high accuracy using only a small portion of the data. We introduce leverages to reflect individual differences in the samples from a statistical perspective. Two kinds of estimators, the leverage-based estimator, and the sketch estimator (a "rough picture" of the aggregation answer), are in constraint relations and iteratively improved according to the actual conditions until their difference is below a threshold. Due to the iteration mechanism and the leverages, our approach achieves a high accuracy. Moreover, some features, such as not requiring recording the sampled data and easy to extend to various execution modes (e.g., the online mode), make our approach well suited to deal with big data. Experiments show that our approach has an extraordinary performance, and when compared with the uniform sampling, our approach can achieve high-quality answers with only 1/3 of the same sample size.