Social media has become a major driver of social change, by facilitating the formation of online social movements. Automatically understanding the perspectives driving the movement and the voices opposing it, is a challenging task as annotated data is difficult to obtain. We propose a weakly supervised graph-based approach that explicitly models perspectives in #BackLivesMatter-related tweets. Our proposed approach utilizes a social-linguistic representation of the data. We convert the text to a graph by breaking it into structured elements and connect it with the social network of authors, then structured prediction is done over the elements for identifying perspectives. Our approach uses a small seed set of labeled examples. We experiment with large language models for generating artificial training examples, compare them to manual annotation, and find that it achieves comparable performance. We perform quantitative and qualitative analyses using a human-annotated test set. Our model outperforms multitask baselines by a large margin, successfully characterizing the perspectives supporting and opposing #BLM.