A packaging machine and method for filling bags with a supporting structure to which at least one filling box is fastened which includes a conveyor element and to which a weighing device and a filling spout are assigned. A control device is provided. The filling box is retained non-communicating with the supporting structure and the assigned filling box and is weighed separately by the assigned weighing device to discharge from the filling box a predefined quantity of intended fill product by way of differential weighing and to fill it into the bag through the filling spout. The control device controls the strength of a volume flow into the bag over the time of the filling process so that the intended fill product is maintained at a high fill height while overflow is simultaneously prevented.