Recent deep learning models for intracranial hemorrhage (ICH) detection on computed tomography of the head have relied upon large datasets hand-labeled at either the full-scan level or at the individual slice-level. Though these models have demonstrated favorable empirical performance, the hand-labeled datasets upon which they rely are time-consuming and expensive to create. Further, given limited time, modelers must currently make an explicit choice between scan-level supervision, which leverages large numbers of patients, and slice-level supervision, which yields clinically insightful output in the axial and in-plane dimensions. In this work, we propose doubly weak supervision, where we (1) weakly label at the scan-level to scalably incorporate data from large populations and (2) model the problem using an attention-based multiple-instance learning approach that can provide useful signal at both axial and in-plane granularities, even with scan-level supervision. Models trained using this doubly weak supervision approach yield an average ROC-AUC score of 0.91, which is competitive with those of models trained using large, hand-labeled datasets, while requiring less than 10 h of clinician labeling time. Further, our models place large attention weights on the same slices used by the clinician to arrive at the ICH classification, and occlusion maps indicate heavy influence from clinically salient in-plane regions.