  The purpose of this paper is to prove that a primitive Hilbert cusp form
$\mathbf{g}$ is uniquely determined by the central values of the Rankin-Selberg
$L$-functions $L(\mathbf{f}\otimes\mathbf{g}, \frac{1}{2})$, where $\mathbf{f}$
runs through all primitive Hilbert cusp forms of weight $k$ for infinitely many
weight vectors $k$. This work is a generalization of a result of Ganguly,
Hoffstein, and Sengupta to the setting of totally real number fields, and it is
a weight aspect analogue of the authors recent work.
