In this chapter we discuss weighted bankruptcy problems, which allow us to represent agents with claims to different amounts and of varying strengths. In Sect. 9.1, we discuss the relation between weighted bankruptcy problems and related resource allocation problems. In Sect. 9.2, we discuss various allocation rules for weighted bankruptcy problems that have been proposed in the literature. These rules are all defined as generalizations of the allocation rules for the bankruptcy problems that we discussed in the previous chapter. After that, we fully concentrate on the absolute priority rule \(P^\dagger \) , which has been proposed as a generalization of the proportional bankruptcy rule \(\mathbb {P}\) . In Sect. 9.3 we explain how \(P^\dagger \) can be characterized in terms of axioms that can be justified of a conception of fairness that has been articulated by Wintein (A Theory of Fairness from Consistency. Theory and Decision, 2025). Indeed, we argue that fairness requires that, for weighted bankruptcy problems, we apply \(P^\dagger \) . We conclude Sect. 9.3 by commenting on alternative characterizations of \(P^\dagger \) .