I would run the truck through by itself so you can have all your data.
As for the truck feeling that way - when was your last alignment (at least check)? Are you running e rated tires? If so, call the manufacturer or find the inflation load chart to see what PSI you should be at to at least match the load rating of the stock tires. For my Toyo AT3s I need to run 44 just to match the Grabber SLs. I am currently running about 48 cold (around 50/51 warmed up). I added air bags around the same time I switched tires, but I can say it was a world of difference between this tow and my tows without bags and while having the RAS setup.
So, the first thing I'd do is check your tire PSI and see how that feels. You're good on all your weight limits.
For comparison, heres what my truck was before attaching the trailer (loaded with people, pets, cargo, and WDH without bars).