Actually John... for some classes of air travel the FAA assumes that the standard passenger weighs 170 pounds.. the ramp agent does a weight and balance calculation for the aircraft and the pilot is responible for checking it.
Some of the smaller aircraft in regional service are very sensitive to weight and balance issues... and I have seen seating on those flights rearranged to get the big folks in the right spots in the cabin.... all so the plane wont crash. It's some silly nonsense about weight, moment and leverage and having enough elevator authority to pick the nose up.
Weight and balance is necessary for all planes. It is a matter of multiple "lever arm" equations. This includes "consumables", i.e. fuel and oil. Fuel burn during flight may have require compensation.
The C.G. (Center of Gravity) will move fore and aft of the "Datum" or reference mark. The actual C.G. and the Datum do not necessarily coincide; for convenience, the Datum can located in the cockpit. But adjustment is done against the Datum, regardless. Original Design criteria generally place the C.G. along the centerline of the wings, from one wingtip to the other. There is an "envelope" in which it is safe to fly: if it goes outside the limits, YOU DO SOMETHING. Same thing for a simple "over Gross" weight. A slight "aft CG" can result in a noticeable fuel savings.
Transport planes have a "loadmaster" who does nothing but this. From the earliest days, there were calculators for this, i.e. the Singer LibraScope; now they all use laptops. Passenger liners use similar techniques.
As a pilot, I was taught to use 180 pounds for a "standard passenger"; I've handled the FAA "standard gun" and the FAA "standard bomb". The FAA likes to have everything classified. If things look too far off "standard", pilots discretion will have to adjust the nominal weight & balance assumptions.
You don't always catch everything: a friend of mine flew a Lockheed Constellation charter once. They nearly kissed the fence on takeoff roll and burned fuel like nobody's business. Nobody tumbled to the fact that it was a BOWLER'S CONVENTION until they landed. Then a passenger dropped a bowling ball almost on my friends toe: 70 guys w/ 2 or 3 16 pounders each!!!
So ... would I be a bastard if I offered this person a draft cross horse to ride? After all that Belgian cross I have to offer 'screams' fat guy please.. or whould it be inhumane on my part to let the fellow tag along in a horse drawn wagon? There are limits. Big folks dont ask to be big... but not all accommodations can deal with the stress.
Sorry, but safety and physics preclude being sensitive or "politically correct" at times. I'm watching my weight so I can take helicopter lessons: 220 pounds weight limit. Screw up in one of those and you're a smokin' hole in the ground.
Mustang