You NEED to read the mfr plate on the trailer, usually front ,left of the deck !!! Never, EVER rely on the seller's mouth !!! The 'standard' for 'trailer weight' is the TOTAL limit...typical car haulers are 7K (7000#). A rule of thumb is a 5 bolt axle is 3500# , so 2 axles = 7000#. And yes you MUST subtract the weight of the entire trailer to figure out true 'payload' capacity. Also check the tires for THEIR rating. Most 14/15" tires should be good for 1700# BUT you NEED to read them !!
Up here the SCAM mfrs do is rate their trailers for 2990# even though you could carry 7000#. They do this to NOT have to add brakes and battery braking systems which cost them $$$.
EVERY tandem axle trailer up here HAS to have 1 set of brakes and of course if ebrakes, battery system. I prefer to have brakes on BOTH axles. It's a huge safety net, especially when you see all teh IDIOT drivers you have to avoid !!
A 16' trailer is fine,though I don't know what the upgrade cost to 18' would be , it is something to consider. Also be sure to have backup lights on the trailer ! it's $50 very well spent !!