Being able to tow a trailer is one thing. Being able to tow a trailer SAFELY is another. As you approach the physical limitations of your tow vehicle, there is less and less room for error. Remember, your TT weighs 6640 empty. Let's say your fresh water tank is 30 gallons.....there's an extra 240 lbs right there. Plus luggage, camping gear, clothing, etc...and it all adds up pretty quickly.
Now....does 7701 lbs mean instant failure while 7699 is OK? Of course not. And under ideal circumstances, you're probably OK. But lets say you're coming home from your trip and the nice weekend turns into a 45 mph crosswind coming home. No problem, you just slow down, right? Now how about the semi trucks coming the other way? Suddenly you find your overloaded truck dealing with a nasty trailer sway that you may not be able to recover. Not good.
Also remember, just because you can get it moving doesn't necessarily mean you can get it stopped. Sure, you plan on driving on relatively flat surfaces....but suddenly all your camping buddies start bragging about this great spot up in the hills....and you find yourself wanting to check it out. So you give it a shot. The F150 begrudgingly drags it up the big hill at 20 mph and you get there. Coming back down the hill, despite having trailer brakes and gearing down, you find the pedal starting to get soft. 1/2 way down the hill you start smelling that nasty burnt bacon smell of overheated brakes, and the pedal is approaching the floor as the fluid boils. Not good.
And even on your fairly level roads.....your cruising along when someone blows a stop sign and you have to make a panic stop.....and your trailer is suddenly right up your.....uh.....bumper....as it sends the overloaded truck careening into the unfortunate car...
I care about your safety. Buy a lighter trailer or a bigger truck. JMHO, of course, some will disagree.