In this paper we study weight homology of singular schemes. Weight homology is an invariant of a singular scheme defined in terms of hypercoverings of resolution of singularities. Our main result is a McKay principle for weight homology of quotient singularities, i.e., we describe weight homology of a quotient scheme in terms of weight homology of an equivariant scheme. Our method is to reduce the geometric McKay principle for weight homology to Kato's cohomological Hasse principle for arithmetic schemes. The McKay principle for weight homology implies the McKay principle for the homotopy type of the dual complex of the exceptional divisors of a resolution of a quotient singularity. As a consequence we show that the dual complex is contractible for isolated quotient singularities.