One of the most popular indicators is the weighted hypervolume indicator. It allows to guide the search towards user-defined objective space regions and at the same time has the property of being a refinement of the Pareto dominance relation with the result that maximizing the indicator results in Pareto-optimal solutions only. In previous work, we theoretically investigated the unweighted hypervolume indicator in terms of a characterization of optimal -distributions and the influence of the hypervolume鈥檚 reference point for general bi-objective optimization problems. In this paper, we generalize those results to the case of the weighted hypervolume indicator. In particular, we present general investigations for finite , derive a limit result for going to infinity in terms of a density of points and derive lower bounds (possibly infinite) for placing the reference point to guarantee the Pareto front鈥檚 extreme points in an optimal -distribution. Furthermore, we state conditions about the slope of the front at the extremes such that there is no finite reference point that allows to include the extremes in an optimal -distribution鈥攃ontradicting previous belief that a reference point chosen just above the nadir point or the objective space boundary is sufficient for obtaining the extremes. However, for fronts where there exists a finite reference point allowing to obtain the extremes, we show that for to infinity, a reference point that is slightly worse in all objectives than the nadir point is a sufficient choice. Last, we apply the theoretical results to problems of the ZDT, DTLZ, and WFG test problem suites.