Interpretability of deep learning (DL) systems is gaining attention in medical imaging to increase experts' trust in the obtained predictions and facilitate their integration in clinical settings. We propose a deep visualization method to generate interpretability of DL classification tasks in medical imaging by means of visual evidence augmentation. The proposed method iteratively unveils abnormalities based on the prediction of a classifier trained only with image-level labels. For each image, initial visual evidence of the prediction is extracted with a given visual attribution technique. This provides localization of abnormalities that are then removed through selective inpainting. We iteratively apply this procedure until the system considers the image as normal. This yields augmented visual evidence, including less discriminative lesions which were not detected at first but should be considered for final diagnosis. We apply the method to grading of two retinal diseases in color fundus images: diabetic retinopathy (DR) and age-related macular degeneration (AMD). We evaluate the generated visual evidence and the performance of weakly-supervised localization of different types of DR and AMD abnormalities, both qualitatively and quantitatively. We show that the augmented visual evidence of the predictions highlights the biomarkers considered by experts for diagnosis and improves the final localization performance. It results in a relative increase of 11.2+-2.0% per image regarding sensitivity averaged at 10 false positives/image on average, when applied to different classification tasks, visual attribution techniques and network architectures. This makes the proposed method a useful tool for exhaustive visual support of DL classifiers in medical imaging.