We present a fast high-resolution fiber Bragg grating sensing system for weigh-in-motion (WIM) application. The proposed system makes use of standard telecom photonics components operating at high speed and with insufficient resolution; then, using signal processing we artificially improve the accuracy of the system down to 1 με. This way, the proposed architecture overcomes the state of the art of optical systems for WIM, which cannot cope with both high resolution and high frequency requirements. The developed system has been applied to a prototype weigh-in-motion device, which consists of a road speed bump. Structural deformations of the bump when perturbed by a thin-footmark load are well reproduced. Using multiple Bragg grating sensors, it is possible to unambiguously determine position and weight of a moving load on the bump with accuracy of 0.2 - 1.2 kg.