I have the same truck as you and I tow what I have in my signature below. It usually weighs around 6300 lbs. once it's loaded up for camping. I have my wife and 5 year old daughter as passengers and I stay below the payload ratings but it's close.
I find it a "comfortable" tow but you can tell it's back there. Just make sure you have a decent WDH with some sort of sway control and you'll be alright up to the 7000 lb. range. I have a standard WDH with 1000 lb. bars and 2 friction sway controls and I've never had sway issues.
If I had a trailer that weighs more than 7500 lbs. I'd be looking at an F250 for sure.
