My little 22' TT (measured from bumper to hitch) weighed #3400 dry... It weighs every bit of it's #5000 GVWR when I've got it loaded and that's with a full water tank, but that's only 30 gallons, so only around #260.. Not really enough to worry about, and if it is, you don't have enough tow vehicle..
I towed it with a 97 F150 with a 5.4 V8 in it and was a good match.. Couldn't imagine towing it with a V6 short wheelbase Jeep Liberty...
I guess since you now own it, all you can do is hitch it up and see how it goes...
Be safe!
Mitch