First of all, keep your speed below 65. Slower if you can manage it. That trailer weighs WAY more than your tow vehicle! What do you have in the back of the trailer? In cases like this weaving and road buck are caused by too heavy a rear. When you are driving and the trailer hits a bump, expansion joint, or some other obstacle in the road it acts like a see-saw. Then it will wag its tail because it has become unstable. Semis passing you will first push the trailer away than draw it in, causing the trailer to REALLY wag its tail! Move everything you can forward. No boxes, no coolers, no cargo in the rear of the trailer. Stow it forward. If this trailer is a toybox, the heaviest vehicle in the back should be all the way forward. That is why your dinette folds up.

If all you haul is motorcycles, then as many as possible should be, again, all the way forward. I don't care how many axles you have.
Your Suburban is not a truck, it's a heavy-duty stationwagon. I
know you
don't want to hear that, but it's the truth. A Suburban is built to ride and handle nice for the wife and kids. If you want it to behave like a truck, it must be equipped for it. Air shocks are not the solution for a heavy trailer. They are for a heavy load
in the Suburban. Heavier shocks would likely help considerably with stability, front and rear. The car should be level, if not a touch tail high, before attaching the trailer.
As to your WDH; you might need heavier bars. Particularly with a toybox. An anti-sway bar works wonders as well. I have a '54 Spartan that's 43' long and the old tart flirts with every semi that passes me. The anti-sway bar calms her down considerably!
Here's a hint from Heloise: Trailers have two weights: dry and maximum load. Load your trailer as if you are going for a big weekend. You can put the coolers in with some dumb-bells in them to approximate the weight of being full. Take it down to the local scales and weigh it. Then you know for sure what it weighs. You would be surprised how much your 'stuff' weighs! Kind of like when Lucy and Ricky took the New Moon over the Continental Divide. You may not be planning a trip like that, but you still need to know what your liability is.
Rent/buy the Long, Long, Trailer. Listen carefully to Ricky (Nicky Collini) because he hilariously goes over this with Lucy (Tracy Collini)
numerous times. Provided of course you Love Lucy.

