I have witnessed the FAA take every single item out of an aircraft, weigh it, compare it to the W&B you are required to keep in the airplane. Ground the aircraft and fine the pilot $10,000. They were in a mood about a separate incident and totally hammered the guy. They can do that any time they feel like it. If you think they don't have scales, guess again. BTW, it is $10,000 per incident, which can be each flight overweight for example. Not having an un-damaged capacity sticker next to your fuel filler. They can and frequently do go and start looking for every single violation they can write. You see, you can barging down the fine. So they make it fairly stout to begin with. I do consulting from time to time on FAR violations. The Navy in its infinite wisdom sent me to Naval Postgraduate School in Aviation Accidents and Safety/Regulations. Makes a bit of coin every couple of years, enough for very expensive hobbies.
Weight and balance is a serious matter in manned airplanes. Lives are at stake. (A few years ago at the local airstrip, four hefty fellows loaded themselves into a Cherokee 140 with nearly full tanks on a summer day and tried to take off. The result was predictable.)
Have you heard of any instances of drones being examined by the FAA, even for issues other than gross weight?