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The field of Weakly Supervised Learning (WSL) has recently seen a surge of popularity, with numerous papers addressing different types of "supervision deficiencies", namely: poor quality, non adaptability, and insufficient quantity of labels. Regarding quality, label noise can be of different types, including completely-at-random, at-random or even not-at-random. All these kinds of label noise are addressed separately in the literature, leading to highly specialized approaches. This paper proposes an original, encompassing, view of Weakly Supervised Learning, which results in the design of generic approaches capable of dealing with any kind of label noise. For this purpose, an alternative setting called "Biquality data" is used. It assumes that a small trusted dataset of correctly labeled examples is available, in addition to an untrusted dataset of noisy examples. In this paper, we propose a new reweigthing scheme capable of identifying noncorrupted examples in the untrusted dataset. This allows one to learn classifiers using both datasets. Extensive experiments that simulate several types of label noise and that vary the quality and quantity of untrusted examples, demonstrate that the proposed approach outperforms baselines and state-of-the-art approaches.