Gravity models are extensively used tools to understand mobility, providing an approximation of the volume of a flow as a function of distance and local population density. Specific gravity models have been designed for studying bike sharing systems (BSS) in urban areas. In this paper, we show how robustness to scale change in data pre-processing can be used as a criterion to select the best model for BSS usage, in addition to the usual criteria of quality of fit. In a second stage, the study the recent evolution of BSS use in large cities via a dynamical application of gravity models over rolling time windows. Exploiting the good interpretability of gravity models, this methodology produces a time series for each parameter, that can be analysed to study the evolution of local policies and users habits.