Answer Sentence Selection (AS2) models are core components of efficient retrieval-based Question Answering (QA) systems. We present the Reference-based Weak Supervision (RWS), a fully automatic large-scale data pipeline that harvests high-quality weakly- supervised answer sentences from Web data, only requiring a question-reference pair as input. We evaluated the quality of the RWS-derived data by training TANDA models, which are the state of the art for AS2. Our results show that the data consistently bolsters TANDA on three different datasets. In particular, we set the new state of the art for AS2 to P@1=90.1%, and MAP=92.9%, on WikiQA. We record similar performance gains of RWS on a much larger dataset named Web-based Question Answering (WQA).