Weak supervision enables efficient development of training sets by reducing the need for ground truth labels. However, the techniques that make weak supervision attractive -- such as integrating any source of signal to estimate unknown labels -- also entail the danger that the produced pseudolabels are highly biased. Surprisingly, given everyday use and the potential for increased bias, weak supervision has not been studied from the point of view of fairness. We begin such a study, starting with the observation that even when a fair model can be built from a dataset with access to ground-truth labels, the corresponding dataset labeled via weak supervision can be arbitrarily unfair. To address this, we propose and empirically validate a model for source unfairness in weak supervision, then introduce a simple counterfactual fairness-based technique that can mitigate these biases. Theoretically, we show that it is possible for our approach to simultaneously improve both accuracy and fairness -- in contrast to standard fairness approaches that suffer from tradeoffs. Empirically, we show that our technique improves accuracy on weak supervision baselines by as much as 32\% while reducing demographic parity gap by 82.5\%. A simple extension of our method aimed at maximizing performance produces state-of-the-art performance in five out of ten datasets in the WRENCH benchmark.