Loading and C of G
There are two aspects to Loading, the weights and their distribution, and you sometimes get some nasty surprises—some fuel tanks have unusual shapes, so you won't get a straight line variation; every fuel load will have a different figure, principally because the fuel tanks have a C of G system all of their own, running separately from the aircraft. There may be enough of a difference to cause an insurance company to have qualms about paying up if you have an accident.
Basic Weight is that of the aircraft as stated on the Weight and Centre of Gravity Schedule (in the Flight Manual or the aircraft docs). This is found by actual weighing before the machine is used for commercial air transport, and every 4 years after.
The Maximum Takeoff Weight is that in the Flight Manual. Any maximum take-off weight less than the full maximum due to performance factors is known as the Restricted (or Regulated) Takeoff Weight (RTOW) and is the starting point for calculating maximum payload available. Sometimes, of course, RTOW is the same as MTOW.
It’s well known that all aircraft will fly overweight to a certain extent, if only because there’s a tolerance range in the performance figures– ferry flights frequently do so, with the extra weight being fuel, but having the physical ability doesn’t mean that you should. You will at some stage be under some pressure to take an extra bit of baggage or top up with that bit of fuel that will save you making a stop en route, but consider the implications. Firstly, any insurance cover will be invalid if you don’t fly within the limits of the flight manual, and, secondly, you will be leaving yourself nothing in hand for turbulence and the like, which will increase your weight artificially. The designer will have allowed for 60-degree turns all the way up to MAUW, but not heavier than that.