In this work, we propose a deep U-Net based model to tackle the challenging task of prostate cancer segmentation by aggressiveness in MRI based on weak scribble annotations. This model extends the size constraint loss proposed by Kervadec et al. 1 in the context of multiclass detection and segmentation task. This model is of high clinical interest as it allows training on prostate biopsy samples and avoids time-consuming full annotation process. Performance is assessed on a private dataset (219 patients) where the full ground truth is available as well as on the ProstateX-2 challenge database, where only biopsy results at different localisations serve as reference. We show that we can approach the fully-supervised baseline in grading the lesions by using only 6.35% of voxels for training. We report a lesion-wise Cohen's kappa score of 0.29 ± 0.07 for the weak model versus 0.32 ± 0.05 for the baseline. We also report a kappa score (0.276 ± 0.037) on the ProstateX-2 challenge dataset with our weak U-Net trained on a combination of ProstateX-2 and our dataset, which is the highest reported value on this challenge dataset for a segmentation task to our knowledge.