A new transmissibility-like index defined as the ratio of the frequency responses of the same monitoring location under two different loading conditions was proposed for Gross Vehicle Weights (GVWs) monitoring in this study. Based on the theoretical finding that the displacements of a beam subjected to moving loads were the convolution of the load and the influence line, the equivalence between the transmissibility-like index at the zero frequency and the ratio of two GVWs under two-moving-load scenarios was theoretically revealed. Given the reference responses for known moving loads, an influence line-free algorithm was proposed to estimate the GVW of an arbitrary vehicle by making full use of the unique property of the new transmissibility-like index. To accommodate various uncertainties and fuse the measurements of different channels simultaneously, the problem of Bridge Weigh-In-Motion (B-WIM) was formulated in the framework of Bayesian inference with the aid of a complex Gaussian ratio probabilistic model of transmissibility function. The posterior distribution of the GVW was derived analytically. By applying the proposed transmissibility-like index, this method possessed an obvious advantage in achieving robust GVWs without the requirement of any knowledge of the bridge model such as the influence line. Two applications, including a numerical example and an experimental verification, were used to demonstrate the efficiency and accuracy of the statistical and influence line-free B-WIM scheme.