If you're asking me then YES they should be charged extra. Being overweight is a choice. I know, I have to fight my weight constantly. I've reached the age where air is fattening. I only breathe every other day.
I loved your use of the double A in FAAT. Have you ever seen the back of a seat belt extension? Printed in raised letters in the plastic is the statement "Conforms to FAA TSO." (hint: remove the space in the middle.)
A friend of mine in Dallas who is not in the airline business made the observation recently that anymore there are five sizes of airline passengers: small, medium, large, extra-large, and omigod it's moving our way! Anyone who takes up more than the seat they purchased should have to pay extra. We are selling space on the airplane. You should pay for the space you take.
Note that the article said that the average 10 pounds that the American public has gained in the past years (personally, I would have guessed more) costs the airlines an extra $350 million/year in fuel costs. If we can't charge more, we should look at changing the weight restriction formula. I think it currently assumes 150 lbs for each adult. FALSE ASSUMPTION!