In this paper, we analyse patterns in face shape variation due to weight gain. We propose the use of persistent homology descriptors to get geometric and topological information about the configuration of anthropometric 3D face landmarks. In this way, evaluating face changes boils down to comparing the descriptors computed on 3D face scans taken at different times. By applying dimensionality reduction techniques to the dissimilarity matrix of descriptors, we get a space in which each face is a point and face shape variations are encoded as trajectories in that space. Our results show that persistent homology is able to identify features which are well related to overweight and may help assessing individual weight trends. The research was carried out in the context of the European project SEMEOTICONS, which developed a multisensory platform which detects and monitors over time facial signs of cardio-metabolic risk.