For every number someone throws out as being where you "need" a certain truck, 10 other people are going to say it's wrong.
Really it's more of a "feel" thing, but very few people have the money to keep buying trucks until they find the one that they're comfortable with.
For sure with the numbers you give, a 3/4 ton truck will tow it comfortably. One of the higher-rated 1/2 ton pickups (i.e. "max/HD payload package") may also work well for you, but do you really want to drop a bunch of money on a new truck only to find out that it isn't significantly better than what you have now?
A 3/4 ton is GUARANTEED to be significantly better.
During camping season, about once a week someone will come on this forum and post a thread after having gone and picked up their new 3/4 ton truck. You would think you were at an Evangelical church service, and hearing them TESTIFY, "Lawdy, Lawdy, I have seen THE LIGHT!"