Just out of curiosity I went an looked at Toyota's webpage for the Highlander. The only trailer they show it hooked to is a teardrop.
Couple of item to think about. No one ever pulls an empty trailer. Dry weights in a brochure are also just a guess and unless you are reading the sticker on the actual unit it's just an educated guess. So the 2,700-2,800# trailer is probably 3,500# with batteries, propane, and their personal items and food. Which is 400# on the hitch. The other is the profile of the trailer. A low riding trailer like a pop up is much different than a 10' tall TT.
2015 Highland tow specsYou have about 1,500# of cargo capacity by the website and you need an XLE or Limited to tow the 5,000#. The TT will take 500# (with WD hitch) which leaves less than 1,000#, possibly a lot less for passengers and other stuff depending upon actual vehicle options. Would have to weigh the Highlander to be sure of you actual capacities.
Personal opinion: Some vehicles are designed to haul people and the trailer is an after thought. A small trailer to do yard projects is one thing but a TT is a whole separate critter.