The present invention relates to a load cell operable with a vehicle having a chassis and a container carried by the chassis, with the load cell supported by the chassis and supporting the container for measuring the weight of the container and any load therein, and to a system having a plurality of these load cells on a vehicle, and to a method of executing weight measurements of loads in a container of a vehicle. The load cell includes a plurality of strain gauges and coupling elements in a floating mount configuration for coupling the load cell to the container and to the chassis in a dual shear beam loading configuration, while limited translational movement is permitted of the load cell relative to the container or the chassis. The load cell also has an electrical interface for receiving analog output data from the strain gauges, adaptively filtering this data and outputting a digital signal representative of the weight of the container and any load therein. This invention permits measurement of incremental loads with sufficient accuracy to permit customer billing based on the measurements.