A method for weighing vehicles moving on a bridge deck pavement is provided. At least one vibration sensor is mounted on a lower side of the pavement to sense low frequency pavement vibrations generated by moving vehicle wheels and propagated in waves in the pavement. Vibration sensor output signals are provided to a computing device. Sensed vibration energy rate is computed and, with signals from vibration sensors mounted at two locations separated by a known longitudinal distance, vehicle speed is also computed. The weight of the vehicle is determined as the product of a calibration coefficient and the ratio of sensed vibration energy rate to velocity. Using vibration sensor signals indicative of wheel generated vibrations in the very near field and summing vibration energy rates computed from these signals during vehicle passage over the vibration sensors the weight of individual vehicles is computed when other moving vehicles are present.