First. Don't ask this same question on RV.net. Those guys will do everything but cuss you out. Its ridiculous overt here when it comes to this topic. Some would even tell you to go get an MDT to be on the safe side.
That being said, this one is close. My F350 SRW has a RAWR of 7000 lbs.. Our Vengeance has a pin weight around 3250 lbs. but that changes a little when the golf cart is in the back. Depending on how much fuel is in the truck, I'm slightly over or under 7000 lbs. on the rear axle. Does it pull well? It pulls like a champ and 70 mph down I-95 headed to Myrtle Beach is no problem. I do have air bags to level things out but that's all. I don't regret the decision at all.
But you're looking at a little more. If the RAWR of the truck you're considering is 7000 lbs., remember you're probably going to be slightly overweight on the axle. My Michelins are rated at 7500 lbs. combined so to me, that's what I consider to be the biggest thing to watch.
As for total weight, I don't fret that too much. Total weight for the whole rig is almost 27,000 lbs. so I'm definitely overweight for a total GCWR. But starting, stopping, and cruising all do very well.
One last thing. Where are you located? Here in NC, DOT won't even think about checking you unless you're doing something obvious like pulling your XLR with an old F150 or something that looks like its about to break underneath the camper.