In this paper approximate weight functions are derived and validated for isotropic and orthotropic double cantilever beams loaded in mode II. The functions define the stress intensity factor at the crack tip due to a pair of point forces acting tangentially on the crack surfaces. They have been deduced using asymptotic matching through finite elements and an orthotropy rescaling technique. The weight functions can be used, along with the related mode I functions [1], to formulate mixed mode fracture problems in beams and plates as integral equations, in terms of stress intensity factors at the crack tip. This approach overcomes the limitations imposed on accuracy by beam/plate theory approximations and it is particularly relevant for those problems where regions of contact and friction and other nonlinear cohesive or bridging mechanisms develop between the crack surfaces as a consequence of structural effects, the action of through-thickness reinforcement or interaction effects between multiple delaminations.