My 24 foot 1984 Lindy on Chevy chassis full of water and loaded up for a trip was just about exactly 10k. Probably had 1k pounds of water and stuff.
My 2019 23 foot Thor is about 11,600 full of water and loaded for a trip including 3 people.
My guess is you will be under 10k with that rig, and probably under 9k if its empty.
You can still get 16.5 tires they are just a little harder to find because there a little less common. Firestone Transforce comes to mind as a reputable brand-name tire that still comes in 16.5 that is available from most any tire shop (if even by special order.) Price is not much more than equivalent 16".