Summary: We show that every regular Bethe ansatz eigenvector of the \(XXZ\) spin chain at roots of unity is a highest weight vector of the \(\text{sl}_{2}\) loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator \(S^{Z}\), and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities regular Bethe roots. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a regular Bethe state.