  We extend our earlier work in [TZ1], where an analytic approach to the
Guillemin-Sternberg conjecture [GS] was developed, to cases where the
Spin^c-complex under consideration is allowed to be further twisted by certain
exterior power bundles of the cotangent bundle. The main result is a weighted
quantization formula in the presence of commuting Hamiltonian actions. The
corresponding Morse-type inequalities in holomorphic situations are also
established.
