Though many algorithms can be used to automatically summarize legal case decisions, most fail to incorporate domain knowledge about how important sentences in a legal decision relate to a representation of its document structure. For example, analysis of a legal case summarization dataset demonstrates that sentences serving different types of argumentative roles in the decision appear in different sections of the document. In this work, we propose an unsupervised graph-based ranking model that uses a reweighting algorithm to exploit properties of the document structure of legal case decisions. We also explore the impact of using different methods to compute the document structure. Results on the Canadian Legal Case Law dataset show that our proposed method outperforms several strong baselines.