Diabetic Retinopathy (DR) is one of the leading causes of preventable blindness in the developed world. With the increasing number of diabetic patients there is a growing need of an automated system for DR detection. We propose Eye WeS, a method that not only detects DR in eye fundus images but also pinpoints the regions of the image that contain lesions, while being trained with image labels only. We show that it is possible to convert any pre-trained convolutional neural network into a weakly-supervised model while increasing their performance and efficiency. EyeWeS improved the results of Inception V3 from 94.9% Area Under the Receiver Operating Curve (AUC) to 95.8% AUC while maintaining only approximately 5% of the Inception V3's number of parameters. The same model is able to achieve 97.1% AUC in a cross-dataset experiment.