Training deep neural networks requires massive amounts of training data, but for many tasks only limited labeled data is available. This makes weak supervision attractive, using weak or noisy signals like the output of heuristic methods or user click-through data for training. In a semi-supervised setting, we can use a large set of data with weak labels to pretrain a neural network and then fine-tune the parameters with a small amount of data with true labels. This feels intuitively sub-optimal as these two independent stages leave the model unaware about the varying label quality. What if we could somehow inform the model about the label quality? In this paper, we propose a semi-supervised learning method where we train two neural networks in a multi-task fashion: a "target network" and a "confidence network". The target network is optimized to perform a given task and is trained using a large set of unlabeled data that are weakly annotated. We propose to weight the gradient updates to the target network using the scores provided by the second confidence network, which is trained on a small amount of supervised data. Thus we avoid that the weight updates computed from noisy labels harm the quality of the target network model. We evaluate our learning strategy on two different tasks: document ranking and sentiment classification. The results demonstrate that our approach not only enhances the performance compared to the baselines but also speeds up the learning process from weak labels.