Word and morpheme segmentation are fundamental steps of language documentation as they allow to discover lexical units in a language for which the lexicon is unknown. However, in most language documentation scenarios, linguists do not start from a blank page: they may already have a pre-existing dictionary or have initiated manual segmentation of a small part of their data. This paper studies how such a weak supervision can be taken advantage of in Bayesian non-parametric models of segmentation. Our experiments on two very low resource languages (Mboshi and Japhug), whose documentation is still in progress, show that weak supervision can be beneficial to the segmentation quality. In addition, we investigate an incremental learning scenario where manual segmentations are provided in a sequential manner. This work opens the way for interactive annotation tools for documentary linguists.