This paper proposes an original and global vision of Weakly Supervised Learning, leading to the design of generic approaches able to handle any kind of labeling noise. A new use case called “Biquality Data” is introduced. It assumes that a small reliable dataset of correctly labeled examples is available, in addition to an unreliable dataset comprising noisy examples. In this framework we propose a new reweighting scheme capable of detecting uncorrupted examples from the unreliable dataset. This algorithm allows learning classifieurs on both datasets. Multiple experiments reproducing several types of labeling noise empirically demonstrate that the proposed algorithm outperforms state-of-the-art competitors.