Looking carefully. GC towing rating with V6 is "only" 6200lb with class 3 hitch. To get to 7400lb you have to step up to V8 or V6 TD and step up in package level to at least Limited or Overland or Summit in order to have load leveling suspension as part of tow prep group IV. It's all kinda fallacy of course. Rated payload for those GCs are less than 1100. to tow safely something on order of 7k you'd certainly wan't wait distribution hitch figure on 100lb in addition of 700lb of tongue weight (at 10%) you talking about only 200-300lb of legal payload left, so basically just a driver. Something goes wrong, like loosing control over trailer, may end up in considerable trouble.
It can be done. Even legally. But really close to maxing out. I would be far more comfortable in full-size.
Tahoe has 1700lb payload and 8400 tow rating with Max Trailering package. Far more comfortable. Even without max trailering you get same 1700 payload, wider stance, longer wheel base, etc.