Your trailer axles have the capacity, but the real story is condition of the trailer and especially the tires. You can overload trailer axles and in most cases get away with it. Overload bad tires and things get tricky very quickly.
A 16' trailer with 2-3500lbs axles is only rated at 3500lbs max WITHOUT trailer brakes, and 7,000lbs ONLY with trailer brakes. You can haul it without brakes and the trailer is mechanically heavy enough no doubt, but get stopped by DPS and he will write you several tickets for over loading(if it has no brakes). Unless you go get Farm tags and then you can get away with hauling 15,000lbs on it without brakes if the springs don't break first.
Also- If you get pulled over DPS/HPD and they do a DOT inspection. You will need some items, check me but I think the following is needed.
Grade 70 transport chain on all four corners (it's the gold colored chain)
Ratchet binders on each chain (not lever binders)
Grade 70 chain on each other item (bucket,mower,tiller,etc) regardless if it's attached to the tractor or not.
Note-Yellow tie downs straps do not meet the regulations.
Check all this with DOT-It's been a few years since I looked it up.
In real life if you have it chained down well, most will let home users go. Commerical users and overloaded trailer get your check book out.