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This paper proposes a novel domain adaptation algorithm to handle the challenges posed by the satellite and aerial imagery, and demonstrates its effectiveness on the built-up region segmentation problem. Built-up area estimation is an important component in understanding the human impact on the environment, the effect of public policy, and general urban population analysis. The diverse nature of aerial and satellite imagery and lack of labeled data covering this diversity makes machine learning algorithms difficult to generalize for such tasks, especially across multiple domains. On the other hand, due to the lack of strong spatial context and structure, in comparison to the ground imagery, the application of existing unsupervised domain adaptation methods results in the sub-optimal adaptation. We thoroughly study the limitations of existing domain adaptation methods and propose a weakly-supervised adaptation strategy where we assume image-level labels are available for the target domain. More specifically, we design a built-up area segmentation network (as encoder-decoder), with an image classification head added to guide the adaptation. The devised system is able to address the problem of visual differences in multiple satellite and aerial imagery datasets, ranging from high resolution (HR) to very high resolution (VHR). A realistic and challenging HR dataset is created by hand-tagging the 73.4 sq-km of Rwanda, capturing a variety of build-up structures over different terrain. The developed dataset is spatially rich compared to existing datasets and covers diverse built-up scenarios including built-up areas in forests and deserts, mud houses, tin, and colored rooftops. Extensive experiments are performed by adapting from the single-source domain, to segment out the target domain. We achieve high gains ranging 11.6%-52% in IoU over the existing state-of-the-art methods.