The high cost of generating expert annotations, poses a strong limitation for supervised machine learning methods in medical imaging. Weakly supervised methods may provide a solution to this tangle. In this study, we propose a novel deep learning architecture for multi-class classification of mammograms according to the severity of their containing anomalies, having only a global tag over the image. The suggested scheme further allows localization of the different types of findings in full resolution. The new scheme contains a dual branch network that combines region-level classification with region ranking. We evaluate our method on a large multi-center mammography dataset including 3,000 mammograms with various anomalies and demonstrate the advantages of the proposed method over a previous weakly-supervised strategy.