I heard of people putting larger tires on their trailers, but I don't see what advantage that has. If it's a 5er, I can see where that would raise the hitch pin some, giving more clearance for the bed rails of the truck. But on a TT, it will raise your center of gravity slight higher which will affect the towing of the trailer, and everything else you indicated. Unless you are on the road 24x7, more than likely your tires will end up dry-rotting on you (regardless of size) long before they wear tread down. Unless your tires are due for a change, (if it were me), I'd keep what I've got until its time to change, then consider going larger. If your wanting to go larger, just to go larger, think you'll get less wear on a larger tire, like I said, they'll dry rot on you before the tread wears down. So keep what you got. My 2 cents ....
Edit, if it's a wider tire, same diameter, I don't think it will change the overall performance of the tow much. And it will dry rot just the same.