7000 limit would be the bare minimum for me towing my 5800 dry trailer. My limit now is 7200. I added Sumo Supersprings before I ever towed the trailer. The Suburban does really better than I expected. I would suggest that there's plenty of big enough trailers under the weight you're suggesting. The new-ish 1500 Chevy/GMCs are the way I would go for what I'm currently pulling. I have been pleased with the Suburban. It converted me from strongly preferring Fords..LOL..
Truth is, for pulling a camper in the 6-7000 range any of the half ton 5 liters with the tow package and proper limits will do the job. My personal preference would be GM and Ford.
An 8000 pound trailer is a hoss. I'd be looking at a 3/4 ton at that point.