Abstract: In contrast with the traditional single-grained word segmentation (SWS), where a sentence corresponds to a single word sequence, multi-grained Chinese word segmentation (MWS) aims to segment a sentence into multiple word sequences to preserve all words of different granularities. Due to the lack of manually annotated MWS data, previous work train and tune MWS models only on automatically generated pseudo MWS data. In this work, we further take advantage of the rich word boundary information in existing SWS data and naturally annotated data from dictionary example (DictEx) sentences, to advance the state-of-the-art MWS model based on the idea of weak supervision. Particularly, we propose to accommodate two types of weakly labeled data for MWS, i.e., SWS data and DictEx data by employing a simple yet competitive graph-based parser with local loss. Besides, we manually annotate a high-quality MWS dataset according to our newly compiled annotation guideline, consisting of over 9,000 sentences from two types of texts, i.e., canonical newswire (NEWS) and non-canonical web (BAIKE) data for better evaluation. Detailed evaluation shows that our proposed model with weakly labeled data significantly outperforms the state-of-the-art MWS model by 1.12 and 5.97 on NEWS and BAIKE data in F1.