Broad learning system (BLS) is a novel and efficient model, which facilitates representation learning and classification by concatenating feature nodes and enhancement nodes. In spite of the efficient properties, BLS is still suboptimal when facing with imbalance problem. Besides, outliers and noises in imbalanced data remain a challenge for BLS. To address the above issues, in this paper we firstly propose a weighted BLS, which assigns a weight to each training sample, and adopt a general weighting scheme, which augments the weight of samples from the minority class. To further explore the prior distribution of original data, we design a density based weight generation mechanism to guide the specific weight matrix generation and propose the adaptive weighted broad learning system (AWBLS). This mechanism considers the inter-class and intra-class distance simultaneously in the density calculation. Finally, we propose the incremental weighted ensemble broad learning system (IWEB) by utilizing a progressive mechanism to further improve the stability and robustness of AWBLS. Extensive comparative experiments on 30 real-world data sets verfy that IWEB outperforms most of the imbalance ensemble classification methods.