I setup a trailer to tow level loaded (trailer level). Always!.. I doubt the vibration has to do with the trailer not being level, but nevertheless the trailer should be level loaded. There will be some vibration towing an empty trailer... I have a 20ft locally made dual axle 10.4K metal deck trailer which tows great, but I do have more road feedback when the trailer is unloaded and I would not really call that vibration. If you overload the trailer or exceed you truck capacity that can add to your issues. Vibration issues are normally in the tires or potentially maybe the hub bearing..
I run e rated LT 16 inch tires (all season hwy tires) on my trailer and I'm about 5 to 10lbs or so from the max air pressure the tires are rated to run at. I just got back from 3000 mile + trip with the trailer...no issues.
Vibration is normally in the tires as I noted...one tire or multiple tires under inflated, worn or defective tire, warped / damaged wheel. Tires should be close to their proper air pressure rating...even more important with loads, as the tires will heat up if they are under inflated.
I also position my towed vehicle on the trailer where the trailer rides fairly level. I tow with a 2500 pickup and you can buy different trailer ball mounts to position the trailer hitch ball at the proper height, and my trailer has an adjustable coupler too, that I'm moved to level the trailer. Its been my experience that if you have the the loaded / towed vehicle either too far forward or too far to the rear on the trailer you will introduce sway and other poor ride characteristics.
I have marked my trailer so I know exactly where the "sweet" spot is for my LC that I tow to sit at on the trailer, otherwise get the vehicle up on the trailer and move it to where the trailer sits level. Of course you can't have the towing vehicle dragging its @ss and have the trailer pointing down hill that's going to be a problem. Depending on various variables related to your tow rig, the receiver, the trailer ball mount and the trailer coupler you may have to get the trailer sitting nose high before you load it. All depends on your setup.
I tow all things with the trailer setting level loaded (to the extent that I can manage that)