Large-scale machine learning is often impeded by a lack of labeled training data. To address this problem, the paradigm of weak supervision aims to collect and then aggregate multiple noisy labels. We propose a Bayesian probabilistic model that employs optimal transport to derive a ground-truth label. The translation between true and weak labels is cast as a transport problem with an inferred cost structure. Our approach achieves strong performance on the WRENCH weak supervision benchmark. Moreover, the posterior distribution over cost matrices allows for exploratory analysis of the weak sources.