Weakly supervised learning algorithms are critical for scaling audio event detection to several hundreds of sound categories. Such learning models should not only disambiguate sound events efficiently with minimal class-specific annotation but also be robust to label noise, which is more apparent with weak labels instead of strong annotations. In this work, we propose a new framework for designing learning models with weak supervision by bridging ideas from sequential learning and knowledge distillation. We refer to the proposed methodology as SeCoST (pronounced Sequest) -- Sequential Co-supervision for training generations of Students. SeCoST incrementally builds a cascade of student-teacher pairs via a novel knowledge transfer method. Our evaluations on Audioset (the largest weakly labeled dataset available) show that SeCoST achieves a mean average precision of 0.383 while outperforming prior state of the art by a considerable margin.