Existing rating methods estimate bridge loading capacity and demand from secondary actions due to live loads in the primary structural components. In these methods, uniaxial yielding stress is traditionally used to detect component capacity using either stress quantities or shear-moment actions to compute the capacity demand of the bridge. These approximations can lead to uncertainties in load capacity estimation. This article presents the weight-over process (WOP), a novel computer-aided approach to bridge loading capacity evaluation based on tonnage and rating factor estimation. WOP is expected to capture different forms of failure in a more general manner than existing methods. In WOP, a bridge finite element model (FEM) is discretized into many sections and element sets, each containing a single material type, and each assigned a suitable 3D failure criterion. Then, factored gross vehicle weights (GVWs) are incrementally imposed on the bridge FEM with those predefined ultimate unfavored loading scenarios in a manner similar to proof load testing. WOP code runs nonlinear analysis at each increment until a stopping criterion is met. Two representative bridges were selected to confirm WOP’s feasibility and efficacy. The results showed that WOP-predicted values at the interior girders were between those of the conventional AASHTO and the nondestructive testing (NDT) strain measurement methods. That may put WOP in a favorable zone as a new method that is less conservative than AASHTO but more conservative than real NDT testing.