Knowledge-based dialog systems have attracted increasing research interest in diverse applications. However, for disease diagnosis, the widely used knowledge graph (KG) is hard to represent the symptom-symptom and symptom-disease relations since the edges of traditional KG are unweighted. Most research on disease diagnosis dialog systems highly relies on data-driven methods and statistical features, lacking profound comprehension of symptom-symptom and symptom-disease relations. To tackle this issue, this work presents a weighted heterogeneous graph-based dialog system for disease diagnosis. Specifically, we build a weighted heterogeneous graph based on symptom co-occurrence and the proposed symptom frequency-inverse disease frequency. Then, this work proposes a graph-based deep Q -network (graph-DQN) for dialog management. By combining graph convolutional network (GCN) with DQN to learn the embeddings of diseases and symptoms from both the structural and attribute information in the weighted heterogeneous graph, graph-DQN could capture the symptom-disease relations and symptom-symptom relations better. Experimental results show that the proposed dialog system rivals the state-of-the-art models. More importantly, the proposed dialog system can complete the task with fewer dialog turns and possess a better distinguishing capability on diseases with similar symptoms.