Weighing system (FIG. 3, FIG. 6) to weigh items, parcels and the like while they are moving, for example, on a conveyor. A servo amplifier (14) and servo controller (20) are arranged to drive a servo motor in a feedback (15) configuration, and acquire torque sensing signals (17) responsive to commanded acceleration of the conveyor while the item(s) are on board. Preferably, constant acceleration of the item(s) is realized during one or more measurement intervals, and mass is derived by a processor (30) based on the measurement data (FIG. 5). Other embodiments are described for weighing granular and slurry materials (FIG. 7) and for weighing multiple, potentially overlapping, parcels in motion (FIG. 8).