High throughput quantitative analysis of microscopy images presents a challenge due to the complexity of the image content and the difficulty to retrieve precisely annotated datasets. In this paper we introduce a weakly-supervised MICRoscopy Analysis neural network (MICRA-Net) that can be trained on a simple main classification task using image-level annotations to solve multiple more complex auxiliary tasks, such as segmentation, detection, and enumeration. MICRA-Net relies on the latent information embedded within a trained model to achieve performances similar to state-of-the-art fully-supervised learning. This learnt information is extracted from the network using gradient class activation maps, which are combined to generate precise feature maps of the biological structures of interest. We demonstrate how MICRA-Net significantly alleviates the expert annotation process on various microscopy datasets and can be used for high-throughput quantitative analysis of microscopy images.