The purpose of this paper is to prove that a primitive Hilbert cusp form g is uniquely determined by the central values of the Rankin-Selberg L-functions L(f ⊗ g, 12 ), where f runs through all primitive Hilbert cusp forms of weight k for infinitely many weight vectors k. This result is a generalization of the work of Ganguly, Hoffstein, and Sengupta [3] to the setting of totally real number fields, and it is a weight aspect analogue of the authors own work [6].