The proliferation of misinformation, such as rumors on social media, has drawn significant attention, prompting various expressions of stance among users. Although rumor detection and stance detection are distinct tasks, they can complement each other. Rumors can be identified by cross-referencing stances in related posts, and stances are influenced by the nature of the rumor. However, existing stance detection methods often require post-level stance annotations, which are costly to obtain. We propose a novel LLM-enhanced MIL approach to jointly predict post stance and claim class labels, supervised solely by claim labels, using an undirected microblog propagation model. Our weakly supervised approach relies only on bag-level labels of claim veracity, aligning with multi-instance learning (MIL) principles. To achieve this, we transform the multi-class problem into multiple MIL-based binary classification problems. We then employ a discriminative attention layer to aggregate the outputs from these classifiers into finer-grained classes. Experiments conducted on three rumor datasets and two stance datasets demonstrate the effectiveness of our approach, highlighting strong connections between rumor veracity and expressed stances in responding posts. Our method shows promising performance in joint rumor and stance detection compared to the state-of-the-art methods.