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Weakly-supervised learning has attracted growing research attention on medical lesions segmentation due to significant saving in pixel-level annotation cost. However, 1) most existing methods require effective prior and constraints to explore the intrinsic lesions characterization, which only generates incorrect and rough prediction; 2) they neglect the underlying semantic dependencies among weakly-labeled target enteroscopy diseases and fully-annotated source gastroscope lesions, while forcefully utilizing untransferable dependencies leads to the negative performance. To tackle above issues, we propose a new weakly-supervised lesions transfer framework, which can not only explore transferable domain-invariant knowledge across different datasets, but also prevent the negative transfer of untransferable representations. Specifically, a Wasserstein quantified transferability framework is developed to highlight widerange transferable contextual dependencies, while neglecting the irrelevant semantic characterizations. Moreover, a novel selfsupervised pseudo label generator is designed to equally provide confident pseudo pixel labels for both hard-to-transfer and easyto-transfer target samples. It inhibits the enormous deviation of false pseudo pixel labels under the self-supervision manner. Afterwards, dynamically-searched feature centroids are aligned to narrow category-wise distribution shift. Comprehensive theoretical analysis and experiments show the superiority of our model on the endoscopic dataset and several public datasets.