Hitch weight

Payload is how much weight you can add to the suburban itself.
Fuel, passengers, any other load, suitcase, dog food, whatever, including the tongue weight of the trailer. All of this must add up to less than the 'burb's GVWR.

The other really important # is GCWR, gross combined weight rating. IF you start with the burbs GCWR from the tag on the doorjamb or the owners manual, subtract the actual weight of the vehicle and everything in it (above) what is left is the max weight your fully loaded trailer can be.

On the drivers door jamb is a yellow sticker with vital info. It will give us the basic payload rating and help to solve some of the mystery. Report back those numbers to us.

OK....I don't care if I'm sounding dumb here...."payload" is.... hitch weight?
And, I also noticed that the info given for the trailer is "base dry hitch weight"....which is 623# for what we are looking at. This does NOT include battery, WDH, full propane tanks? So...for example, if my allowed hitch weight would be 750#, I would be cutting it too close? Or over? I would rather NOT be close....I would like a lot of wiggle room with weight....even if it means we need to choose a different camper.

OK....this is good information, although a little foreign to me! Our Suburban is a 2007, don't know the rest of the info. My husband drives it, so when it gets home, I will look in the owner's manual for the information above. Just glad I am thinking about this BEFORE buying a trailer. I did think that all Suburbans were basically alike. And, every sales person we have talked to has asked about our tow vehicle. We tell them we have a Suburban, and they just say "Oh, then you will be able to tow anything I would sell you with no problem." I guess this is not true!!!

Its good that you are not trusting the sales person. Some are pretty honest and savvy when it comes to towing. Most are not.

The short answer to this is that, yes, you can tow a trailer with an overall weight of 4000-4500# without any problems. Keep in mind that the 4500# is considering that would be its GVWR, not "dry" weight. In other words its maximum weight that it can be fully loaded.

If the 4500# is the listed dry weight, then you may be pushing it if not over weight. Dry weight is a fictional number. Dry weight is the weight of the trailer before any options are installed, and before any propane tanks or battery is added. A trailer never even leaves the factory weighing its dry weight. And no one tows a trailer that weighs its dry weight.

Also you didn't tell us what year, motor, and gear set your 'Burb has. All of those specs are important because the various towing related numbers change with model years, engine sizes, and gearing.

EDIT: Also, is this a C1500 or a K1500? Usually 4wd drops towing capacity by 500#

Whatever trailer you are looking at, take the gvwr of the prospective trailer and multiply by 13%. That will give you a good idea of what the loaded tongue will weigh. You then need to weigh your tow vehicle unhitched as if fully loaded for camping including passengers, fuel, hitch, pets, gear, etc. Subtract whatever that weight is from the gvwr of the tow vehicle and the difference will be your hitch weight allowance.

v-8 SUV's are infamous at having great towing capacities, but lousy payload amounts. plus they have soft suspensions.

most will run out of payload, WAAYY before they ever come close to their max towing capacity.

so, everyone other than a 150lb. driver, cargo and the WDH, all have to come out of the payload amount.
and since SUV's usually have lots of passengers, their weights end up eating up much of the payload amount.

and the Burb's GVWR is really not that important, as much as its payload amount and the GCWR numbers are.
the Burb's GVWR is just the max it can weigh by itself.

so, yes, you need to post more info on it, like year, rear end ratio, factory tow package or not, 4x4 or 4x2, weights of passengers.

You need to get the spec for your year chassis and motor.
A 2015can pull a 8K trailer with a GVWR of 7.300-7,500 lb

VERY ROUGH ESTIMATE:
Guessing that your loaded trip ready trailer is 6000 lbs. you will have around 780 lbs. of tongue weight.

Keep in mind that this is just a guess, not knowing much about your tow vehicle's payload rating and not knowing much about your new trailer
Basically, "I know nothing."