How far, how often, are the key factors. If you tow it 50 miles to your camping spot at a Yogi Bear campground them bring it home in the fall. That is different from several longer tows each summer.
At this point why guess? You are already going to give it a test drive, so drive to the CAT scales and weight the combo. Unhook the TT and weight the truck.
Then, you will know the true weight and load your truck sees when you are camping. My guess is, it is a lot more than you think. But then again, why guess?
Locally, the process take about twenty minutes and cost $12,00 to $14.00 depending on which truck stop I go to.