Linc,
How much of those 13,000 lbs. was on the 4 rear dually tires?
It's of course important to get detailed enough RV weight data to make sure no tire is over-loaded. Dividing the rear weight by 4 gives an approximate estimate of the weight on each rear tire. Dividing the front weight by 2 gives an approximate estimate of what's on each front tire. Some RV owners even get each corner of their RVs weighed individually for more accurate estimates of each tire's loading.
Large Class C motorhomes can often have their rear weight be too much for the type of rear tire being used and/or the pressure being used in those tires.