The 5.3L 4wd Suburbans came with a max Gross Combined Weight Ratings (GCWR) of 12,000, 13,000, and 14,000 lbs depending on the configuration. This rating is the maximum permissible weight of the truck and trailer combination as it goes down the road. Using just the published curb weight of the truck and the dry weight of the trailer, your combination already exceeds the 14,000lbs limit by 95 lbs.
Your truck will definitely weight more than that published curb weight, especially once loaded up for a trip. The trailer also will weigh significantly more than the published dry weight with the options that you've added. You're talking about being at least 1,500 lbs over your combination weight once loaded up for a trip. That's really over for a light duty truck.
I wouldn't pull that trailer with the truck. Even if it was for very occasional trips. That comes from someone who's not part of the weight police group that's common on this forum. I normally keep my nose out of other peoples combos and weight. I'm the type of person that's ok with pushing the limits, even exceeding them every once in a while. But it's looking like you'll be well beyond the limits constantly. It's to the point of being unsafe and there's a very real concern that you might actually damage the truck with this combo.
Also, don't fall into the money pit thinking that a few bolt-ons here and a few upgrades there will get you by because it won't. That's something that's more effective when you're within your limits. Leveling systems, hitches, suspension upgrades, etc won't increase your tow capacity. The strain on the cooling system, transmission, engine, drive shaft, diff, and axles still exist. When it comes to towing limits it is what it is.
Unless the stickers in your door jamb give more ideal numbers, I would look for a more capable truck for the time being if you still want to get use out of the trailer. A cash beater could do the trick. You only have to drive it for 6 months or so.
