The weight only contacts the back of the film. It leaves a tiny drying mark which can be wiped off with film cleaner on a wipe such as a PecPad.
In festoon drying, noted above and used by some manufacturers, it does leave a mark because the emulsion has just been coated, is not hard yet and is wet. This is different.
Our weights were about 1/8" stainless steel "C" shapes and were just slid over the looped hanging film to keep the film taut.