The camper you are looking at is pretty light. I think you'll probably be ok, but you aren't going to want to tow it up the sierra's fully loaded
What we did our first year is towed with what we had. When I bought my 150 I had no intentions of towing with it, I ended up with the max tow package because it was on the truck we ended up buying, anyway... We were barely within our stickered limits lightly loaded. There were several times when we couldn't take a friend with us, less firewood than we wanted, tanks almost always empty, etc.
Your scaled weights are really all that matters. It's pretty awesome you went to the scale... a lot of people don't.
Running the math (just to confirm or deny the other numbers I've seen on the thread)
Your GVWR according to your sticker is 6113
Your TV loaded, un hitched, weighs .....5364
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= 749 lbs of available payload.
The *dry* hitch weight of the camper you are looking at is only 280 lbs.
You could fully load that camper up to it's own max weight (by adding 620 lbs of 'stuff' in the camper, and you would still be under 750 lbs on the hitch. Editing this post to add something I just realized - The hitch on your truck says '600 lbs' max, but it doesn't indicate if adding a weight distributing hitch changes this. On most Tow vehicles, there is a different rating on the receiver if you are towing with a WDH, and I recommend that you use one
Point stands, I don't see you putting even 600 lbs on that hitch, unless you are over loading your camper.
It looks like you have a cushion of about 200 lbs to play around with, with the trailer included, with your receiver on your SUV being the only potential problem. The only thing I would probably look at in more detail is your rear axle weight rating. If most of your weight in your SUV is sitting on the back axle, that's going to be pretty close to maxed when you trailer up. Find out if a WDH hitch will increase the receiver capacity on your SUV. Because the WDH transfers some of the weight to your front axle, it reduces the *actual* weight of the trailer that is sitting on the rear, thus allowing for more than (600 lbs in your case) on the receiver. It's close even without a WDH.
If it was me... I would be ok with getting the camper you are looking at. I wouldn't get a bigger one.
And full disclaimer. I towed our camper my first year with a truck that was pretty close to the limits as well. We never towed with full tanks, and we had to be careful about what we took with us.
I traded that truck in after the first year, and now have what I believe to be a much better towing experience.
You may have to just go for it, and upgrade your tow vehicle down the road when your situation warrants that move. If I could do it all over again, I would follow that same approach, again, myself.
Good luck with your choice, you've already done a lot more homework than most that are new here, asking the same questions.