An inverse method for the identification of a set of crystal plasticity parameters is introduced and applied to in situ tensile tests on steel polycrystals. Various mean grain sizes are obtained with different conditioning of AISI 316LN austenitic stainless steel. Identification is based on a weighted Finite Element Model Updating (FEMU) using both displacement fields at the microscale and macroscopic load levels. The values of the identified parameters depend on the factor weighing the contributions of the microscopic and macroscopic quantities. On the one hand, surface displacement fields are measured by Digital Image Correlation (DIC). On the other hand, they are simulated by resorting to Finite Element calculations with a local crystal plasticity law (i.e., Méric-Cailletaud's model) and a 2D simulation of the microstructure. The parameters associated with isotropic hardening are calibrated for the different mean grain sizes. The benefits of considering full-field measurements are manifest for instance in the excellent Hall-Petch trend captured at the microstructural scale. The identification procedure is also applied to the estimation of hardening parameters describing the interaction between slip systems.