You might get lucky and see the weight rating of the wheel if you crawl underneath and check. However some wheels ratings' can only be found with the tire off the wheel, as the weights are in the valley between the bead profiles.
With 6,000 lb. axles you could be fine with LT tires, but LT tires are rated for 3042 lbs. AT your GVWR of 14,000 lbs. you ideally would have about 11,200 lbs. distributed equally on all 4 tires, which would equate to 2800 lbs./wheel. That would give you about 200 lbs. of cushion. However if all the tires/wheels are not loaded equally you could be looking at, say 3500 lbs. on one tire with a corresponding lesser amount on other tires. The would put you about 500 lbs. over the weight rating of your tire.
I have weighed all my wheels and discover I have a variation of over 500 lbs. between tires.
With the GVWR of your trailer, without knowing actual weights, I would go with a "G" rated tire. Provided of course that your wheels would handle the increased pressure. I prefer Sailun tires because of the very good service I've gotten from them.