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Source separation is the task of separating an audio recording into individual sound sources. Source separation is fundamental for computational auditory scene analysis. Previous work on source separation has focused on separating particular sound classes such as speech and music. Much previous work requires mixtures and clean source pairs for training. In this work, we propose a source separation framework trained with weakly labelled data. Weakly labelled data only contains the tags of an audio clip, without the occurrence time of sound events. We first train a sound event detection system with AudioSet. The trained sound event detection system is used to detect segments that are most likely to contain a target sound event. Then a regression is learnt from a mixture of two randomly selected segments to a target segment conditioned on the audio tagging prediction of the target segment. Our proposed system can separate 527 kinds of sound classes from AudioSet within a single system. A U-Net is adopted for the separation system and achieves an average SDR of 5.67 dB over 527 sound classes in AudioSet.