Domain adaptation has proven to be suitable for alleviating domain discrepancies, which hinder the generalization capacity of classifiers. Among a few alternatives, domain adaptation techniques that align features in a domain-agnostic space through adversarial learning have been widely investigated. Nevertheless, such an approach often implies the deterioration of feature discriminability as a side effect of the adversarial alignment, which does not take into consideration class labels of the target domain samples. We advocate that weakly-supervised learning can help mitigate that problem, as noisy labels for the target domain samples may serve to sustain class discriminability during the feature alignment procedure. Therefore, in this work we propose a weakly-supervised, adversarial domain adaptation method for a change detection task based on the Domain Adversarial Neural Network (DANN) strategy. We assessed the performance of the proposed method on a deforestation detection application, conducting experiments in sites of the Amazon and Cerrado (Brazilian Savannah) biomes using Landsat-8 images, each site corresponding to a different domain. The results showed that the inclusion of weak supervision in the domain adaptation procedure provided higher accuracies as compared to the original DANN strategy, which did not prescribe any supervision for the selection of target domain samples in the training procedure. On average, the Average Precision and F1-score metrics values increased by 10.1% and 12.6% respectively with the use of the proposed method. Additionally, our method achieved performances that are compatible with the ones obtained with previously proposed, state-of-the-art domain adaptation methods. To the best of our knowledge, the proposed method is the first weakly-supervised domain adaptation strategy conceived for deforestation detection and, in general, for change detection.