Each state does licensing different (although there may be some Federal commercial limits).
Here in Oregon, there is a cutoff at 8,000 lbs GVWR (trailer). Above 8K, they want you to get "T" plates on the tow vehicle. I don't believe that is a commercial designation, but rather taxes.
The DMV doesn't seem to get too picky about trailers up to about 10K being licensed at 8K, but I wouldn't do a 16K or 20K equipment trailer.
A Gooseneck or 5th wheel doesn't matter.
I think there is also a limit that the trailer isn't supposed to be longer than about 35 feet without a CDL.
They also want you to have a CDL if you have air brakes.
Then, I think your combination pickup or truck + trailer must be below 26,000 lbs, otherwise you'll need a CDL.
Look up the local laws. It does give some flexibility. However, if you get a 16K trailer, the trailer itself will be massively heavy, and will reduce your cargo weight somewhat. And, for the 16K trailer, you may need to keep your tow vehicle under 10K.
It seems rare that personal vehicles are forced to get weighed (or fuel dipped). But, if you have a load that looks clearly overweight, they may take some interest in you. Or, of course, if you get in an accident they may take a keen interest in compliance with laws.