The methodology referred as probabilistic surface damage tolerance for aeroengine rotors is used to evaluate the risk of fractures induced by low-cycle failure problems, and fracture mechanical models are usually used to carry out the analysis, in which stress intensity factors (SIFs) need to be calculated. Weight function method (WFM) can help improve the probabilistic surface damage tolerance methodology. The WFM offers remarkable computational efficiency in calculating SIFs for cracks in aeroengine rotors with complex stress gradients that are mainly induced by a local stress concentration or multiple loads, including centrifugal, thermal, and residual stresses. In this case, the universal weight functions (mode I) for surface cracks in three-dimensional finite plates, including flat plates and plates with holes, are presented. The critical step of WFM is to obtain certain coefficients in the universal weight function. Response surface method (RSM) can effectively derive the coefficients determined by multiple geometric parameters, including the length and thickness of a flat plate and the length, thickness, radius of a plate with a hole. Errors between the WFM results and the finite element results are less than within the application scope. Furthermore, a surface damage tolerance analysis of the hole features in the aeroengine rotors based on the abovementioned two types of WFM is conducted. The selection of the weight function influences the SIF results, and the probability of failure (POF) calculated by the applied weight function of the plate with a hole is 2.02% higher than that of the flat plate. The relevant difference, which is determined by the fracture threshold crack size, has a negative relationship with the magnitude of stress distributed on the crack surface.