Speech dereverberation is an important stage in many speech technology applications. Recent work in this area has been dominated by deep neural network models. Temporal convolutional networks (TCNs) are deep learning models that have been proposed for sequence modelling in the task of dereverberating speech. In this work a weighted multi-dilation depthwise-separable convolution is proposed to replace standard depthwise-separable convolutions in TCN models. This proposed convolution enables the TCN to dynamically focus on more or less local information in its receptive field at each convolutional block in the network. It is shown that this weighted multi-dilation temporal convolutional network (WD-TCN) consistently outperforms the TCN across various model configurations and using the WD-TCN model is a more parameter efficient method to improve the performance of the model than increasing the number of convolutional blocks. The best performance improvement over the baseline TCN is 0.55 dB scale-invariant signal-to-distortion ratio (SISDR) and the best performing WD-TCN model attains 12.26 dB SISDR on the WHAMR dataset.