The limiting factor is the payload the Suburban can carry. Typical payload for a 1500 is ~1500 lbs. Subtract the weights of you and your passengers, and your gear/stuff, and that's what's left for your trailer tongue weight.
If you want to do it the right way, load up the family and a bunch of gear, fill the gas tank, and go over to the nearest CAT scale. Subtract the total weight on the slip from 7200, and that's how much you have left for the tongue weight of a trailer. Don't forget to include the weight of the hitch, too.
Depending on the size/weight of your family/passengers, you're probably ok. My first TT was a 29' Trail Cruiser. Dry weight was right around 4500. Drove down to Florida, twice, with no issues - 1200 miles each way. Burb is an '01 half ton. As you can see, I'm awfully close to the 4,000 lb rear axle weight rating, and 7200 lb gross vehicle weight rating.
Here's the rig and weigh slip:

