Hilico,
Thanks for the compliment! My general belief is that when someone truly understands a subject, their explanations get easier to understand. Those who start off an explanation with "it is complicated" are usually telling you "I really don't know the answer, but here goes....."
Also, a good basic premise is that most intelligent people (about 2/3 of the human race, in my book, and maybe virtually all ppruners) can understand almost anything if the explainer understands the subject and wants them to know the answer. Those are two big if's!
Mr. Selfish,
I can't readily understand why the arm times weight does not equal the moment, because it really is that simple. The only possibility is that the as-weighed weight is corrected with standard items (each at a fixed location) to produce a corrected weight and moment, which is then used as the pilot's basis.
For example, if the weighing was done unfueled (often done for new manufacture and when coming out of major maintenance), the mechanic will adjust for "trapped fluids" to achieve the operating zero fuel weight. These trapped fluids include the fuel that is below zero on the gage (unusable fuel).
I wonder if this gets you closer to the answer.