The uniqueness of solutions to boundary value problems are important to understanding real world applications. In this paper, two prominent classes of nabla fractional boundary value problems are investigated and presented with improved weighted norms. This allows the current sufficient conditions in the literature to be relaxed. The approach firstly establishes the equivalent summation representations with their associated Green's functions with the important inherent properties proven relating to these weight norms. The second component of the approach is via the application of the Banach fixed point theorem with sufficient conditions to establish the uniqueness and existence of solutions to the considered problems on well-defined spaces with respect to novel weighted supremum norms. To illustrate the merit, novelty, and applicability of the established results, two examples are presented.