A rear axle weight of 19,500 of course, assumes that the coach is balanced side to side, with an equal distribution of 9,750 pounds left and right (19,500 / 2). A washer dryer on one side combined with a refrigerator/pantry, or poorly loaded basement on that same side could easily cause a noticable, and possibly dangerous imbalance. For example, your left side could weigh 10,050 and the right side would be 9,450 pounds. While your total rear Axle weight is still 19,500 pounds, you have exceeded the axle end limit weight of 10,000 pounds. Remember, the axle end limit weight is half of the total axle gross weight rating. In this case, the Rear GAWR of 20,000 divided by 2 equals 10,000. The tires can handle the weight without any problem, but the axle, with associated bearings and suspension components cannot. Now one would think that the manufacturer would account for this during the design and construction process, and they are getting better at it, but it is the operator who has the end responsibility of proper balance. Weighing each wheel position will give the most accurate information, but it's not always available. A CAT Scale facility is better than not weighing at all, but it has limits. It's up to us to try and balance the load as best we can. And follow the excellent advice of Mr Wolfe once you get those individual wheel position weights.
