The effectiveness of Neural Information Retrieval (Neu-IR) often depends on a large scale of in-domain relevance training signals, which are not always available in real-world ranking scenarios. To democratize the benefits of Neu-IR, this paper presents MetaAdaptRank, a domain adaptive learning method that generalizes Neu-IR models from label-rich source domains to few-shot target domains. Drawing on source-domain massive relevance supervision, MetaAdaptRank contrastively synthesizes a large number of weak supervision signals for target domains and meta-learns to reweight these synthetic “weak” data based on their benefits to the target-domain ranking accuracy of Neu-IR models. Experiments on three TREC benchmarks in the web, news, and biomedical domains show that MetaAdaptRank significantly improves the few-shot ranking accuracy of Neu-IR models. Further analyses indicate that MetaAdaptRank thrives from both its contrastive weak data synthesis and meta-reweighted data selection. The code and data of this paper can be obtained from https://github.com/thunlp/MetaAdaptRank.