Recently, numerous studies have demonstrated the effectiveness of contrastive learning (CL), which learns feature representations by pulling in positive samples while pushing away negative samples. Many successes of CL lie in that there exists semantic consistency between data augmentations of the same instance. In multi-view scenarios, however, CL might cause representation degeneration when the collected multiple views inherently have inconsistent semantic information or their representations subsequently do not capture sufficient discriminative information. To address this issue, we propose a novel framework called SEM: SElf-weighted Multi-view contrastive learning with reconstruction regularization. Specifically, SEM is a general framework where we propose to first measure the discrepancy between pairwise representations and then minimize the corresponding self-weighted contrastive loss, and thus making SEM adaptively strengthen the useful pairwise views and also weaken the unreliable pairwise views. Meanwhile, we impose a self-supervised reconstruction term to regularize the hidden features of encoders, to assist CL in accessing sufficient discriminative information of data. Experiments on public multi-view datasets verified that SEM can mitigate representation degeneration in existing CL methods and help them achieve significant performance improvements. Ablation studies also demonstrated the effectiveness of SEM with different options of weighting strategies and reconstruction terms.