Weakly supervised semantic segmentation has been a subject of increased interest due to the scarcity of fully annotated images. We introduce a new approach for solving weakly supervised semantic segmentation with deep Convolutional Neural Networks (CNNs). The method introduces a novel layer which applies simplex projection on the output of a neural network using area constraints of class objects. The proposed method is general and can be seamlessly integrated into any CNN architecture. Moreover, the projection layer allows strongly supervised models to be adapted to weakly supervised models effortlessly by substituting ground truth labels. Our experiments have shown that applying such an operation on the output of a CNN improves the accuracy of semantic segmentation in a weakly supervised setting with image-level labels.