While collectors often call the marking itself a "waffenamt", the term really means "weapons office". The Heereswaffenamt (Army weapons office) controlled the numerous inspectors who worked at factories and depots in Germany and the occupied countries. An inspector was assigned a number and had a set of stamps with that number on them. He had a small staff who either did the marking or, in most cases, supervised contractor employees who did.
In German factories, the regular civilian employees usually put on the marks, with only minimal supervision by the army. In occupied countries, control and supervision was more stringent.
There seems to be little information on the actual identity of the inspectors, but collectors can often determine when and where an item was made by the inspector number, as well as when he was reassigned.
In the U.S. system, in contrast, the inspector's mark indicates only the commanding officer of the Ordnance District in which the item was made. It is unlikely that Col. Frank J. Atwood (FJA) or Lt. Col. Robert C. Downie (RCD) ever actually picked up a hammer and stamped their initials on a gun, but they were responsible for the quality of the product.
Jim