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With the prevalence of machine learning in many high-stakes decision-making processes, e.g., hiring and admission, it is important to take fairness into account when practitioners design and deploy machine learning models, especially in scenarios with imperfectly labeled data. Multiple-Instance Learning (MIL) is a weakly supervised approach where instances are grouped in labeled bags, each containing several instances sharing the same label. However, current fairness-centric methods in machine learning often fall short when applied to MIL due to their reliance on instance-level labels. In this work, we introduce a Fair Multiple-Instance Learning (FMIL) framework to ensure fairness in weakly supervised learning. In particular, our method bridges the gap between bag-level and instance-level labeling by leveraging the bag labels, inferring high-confidence instance labels to improve both accuracy and fairness in MIL classifiers. Comprehensive experiments underscore that our FMIL framework substantially reduces biases in MIL without compromising accuracy.