AC Weight
According to folks I used to fly DC-8s with the 8s also used to have this type of system installed.
It did work off nitrogen pressure inside the oleo strut.
It was also difficult to maintain and prone to failure. By the time I was flying the planes of these systems had been removed. Of course so had many other useful items like apu's, air conditioning and turbocompressors in some of the planes.
Perhaps the real reason these self weighing systems are not in widespread use today is that operators do not want the crews or the FAA knowing how much weight we are really carrying.