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A quantitative understanding of the dynamics of bee colonies is important to support global efforts to improve bee health and enhance pollination services. Traditional approaches focus either on theoretical models or data-centred statistical analyses. Here we argue that the combination of these two approaches is essential to obtain interpretable information on the state of bee colonies and show how this can be achieved in the case of time series of intra-day weight variation. We model how the foraging and food processing activities of bees affect global hive weight through a set of ordinary differential equations and show how to estimate reliable ranges for the ten parameters of this model from measurements on a single day. Our analysis of 10 hives at different times shows that crucial indicators of the health of honey bee colonies are estimated robustly and fall in ranges compatible with previously reported results. The indicators include the amount of food collected (foraging success) and the number of active foragers, which may be used to develop early warning indicators of colony failure., Comment: 26 pages with 9 figures