This paper addresses weakly supervised amodal instance segmentation, where the goal is to segment both visible and occluded (amodal) object parts, while training provides only ground-truth visible (modal) segmentations. Following prior work, we use data manipulation to generate occlusions in training images and thus train a segmenter to predict amodal segmentations of the manipulated data. The resulting predictions on training images are taken as the pseudo-ground truth for the standard training of Mask-RCNN, which we use for amodal instance segmentation of test images. For generating the pseudo-ground truth, we specify a new Amodal Segmenter based on Boundary Uncertainty estimation (ASBU) and make two contributions. First, while prior work uses the occluder’s mask, our ASBU uses the occlusion boundary as input. Second, ASBU estimates an uncertainty map of the prediction. The estimated uncertainty regularizes learning such that lower segmentation loss is incurred on regions with high uncertainty. ASBU achieves significant performance improvement relative to the state of the art on the COCOA and KINS datasets in three tasks: amodal instance segmentation, amodal completion, and ordering recovery.