Drug use and abuse is a serious societal problem. The fast development and adoption of social media and smart mobile devices in recent years bring about new opportunities for advancing computer-based strategies for understanding and intervention of drug-related behaviors. However, the existing literature still lacks principled ways of building computational models for supporting effective analysis of large-scale, often unstructured social media data. Part of the challenge stems from the difficulty of obtaining so-called ground-truth data that are typically required for training computational models. This paper presents a progressive semi-supervised learning approach to identifying Twitter tweets that are related to personal and recreational use of marijuana. Based on a small, labeled dataset, the proposed approach first learns optimal mapping of raw features from the tweets for classification, using a method of weakly hierarchical lasso. The learned feature model is then used to support unsupervised clustering of Web-scale data. Experiments with realistic data crawled from Twitter are used to validate the proposed approach, demonstrating its effectiveness.