Here we are then. It`s relatively easy to remove the weights, although it tends to be more difficult with the older rolling stock because the composition of the plastic is different and, as a result, the plastic is less flexible. In the late 1990s/early 2000s, concern about a possible carcinogenic material being used in plastics for children`s toys meant that the "recipe" for Playmobil had to be changed and this means that the plastic is now a more flexible. (This is not just a problem for Playmobil, it affects all makers of plastic toys.)
The first picture shows the underside of a truck, the grey rectangle being a cover which holds the weight in place. At each end, two protruding pieces hold the weight in place lengthwise (and you only the two pieces nearer the camera in this picture, but you can just see the tops of the equivalent pieces at the far end). On each side, there are two "stepped" clips which hold hold the weight in place against the bottom of the chassis, so it doesn`t drop off when the truck or carriage is running. (The weight cover is square, although in the picture, perspective makes it look oblong.)
The second picture shows two of the end pieces. They are held tightly against the plastic crosspiece, but they are not clipped to it.
In the third picture, you can see two of the side pieces which have a "step" in them which means that they are clipped under the side frame.