I had 2019 Ram 3500 DRW pickup, did a bed delete and added a steel flatbed, and... well, now I have a 5500. Lets say I was a "little" overweight. Sure, I was probably on the extreme side and you could be more careful, but my rear axle crossed the scales at 13,260 once, and I decided that day to get a new truck.
You could save a lot of weight by going with an aluminum bed, but you will still end up adding a lot of weight with tools and stuff you carry. The math is very hard to make work on a one ton truck.
If you want to do this, save yourself a lot of headache and buy a 5500.
Edit: interesting, everyone who has replied so far has a 450/550 class truck.
Edit 2: photo