We've been towing our Hybrid for the past 6 years with late 90's Suburbans.
Starcraft 239TBS, about as big as a hybrid gets. 6500lbs GVW.
First a 1500, now moved up to a 2500 version. 1500 did fine, but there were some hills that would slow us down to 45 or so. Don't forget, this is with trucks that are almost 25 years old as well.
My FIL tows the same sized hard side with a Ecoboost Ford Expedition, and used an 04 Tahoe before that. He also had a hybrid (Roo 233) he towed with the Tahoe for a few years.
If you make sure it has a real tow package, you should be fine. 2500/3500 Passenger vans are also a great fit if you don't want 4wd. I've seen a few family's using the Nissan NV's to tow campers in our travels.