Such a filling device is known from EP 1 025 424. The known filling device contains one of the standard filler carousels that extend around a substantially vertical axis and are provided on their outer circumference with radially projecting holders for the containers. The holders are normally configured in the form of tongs, the two tong jaws being spring-loaded or magnetically attracted to each other and comprising a recess adapted to the container, with which jaws the holder grips around the container for filling purposes. Normally, bottles are filled that are provided underneath the filling opening, on their neck, with a protruding flange which offers a support on the upper side of the holder. For the filling operation a filling valve is provided that is in coaxial alignment with the filling opening of the container with its outlet in the filling position. A predetermined quantity of the product is filled into the container by operating the filling valve. To control the filled state, the container is weighed. For this purpose a weighing device is provided that contains an elastically deformable element in the form of an elastic bar which is rigidly secured to the frame and the deformation of which, caused by the weight of the container, is detected and evaluated as a measure of the weight. The elastic element is acted upon by the holder, the elastic element and the holder being positioned side by side in radial direction with respect to the rotational axis of the filler carousel. The holder serves as a lever arm for acting on the elastically deformable bar. Due to this horizontally and radially extending arrangement the known weighing device is, however, relatively sensitive to vibrations caused by the operation, which arise due to the rotation of the filler carousel or due to forces, or the like, acting on the container for a short period of time. These vibrations may distort the weighing result.