Tongue weight on average is around 12-13 percent of the actual weight of a TT. If the actual wt. is close to the GVWR, the tongue wt. would be approx. 6700 lbs. I would suggest a cargo weight allowance of 1,000 lbs on top of the dry wt. which would be 6575 lbs. This would mean that the actual wt. on the axles is likely around 6600 lbs. Load range C ST tires have an 1820 max. load capacity rating (at 50 psi) - 3640 per axle. The tires would therefore be loaded to 6600/7280 = 91 percent (9 percent reserve load capacity).
It is recommended that ST tires have a reserve load capacity of 15 percent min. See comments from a tire engineer at RVtiresafety.net. There are no legal requirements for the amount of reserve load capacity and RV manufacturers can get away with loading tires up to their max and it is common for them to do that. Not having a min. of 15 percent reserve load capacity is increasing the risk of a blowout. When we bought our current TT, we ordered the optional Goodyear load range D tires and have about 30 percent reserve capacity and have not had a single issue to date and are now on our 4th season with them.
A TT can also weigh more on one side, usually due to a slide out. Going to a scale would be a good idea so that an owner knows where they stand on weights.
The axles on that Trail Runner would be loaded to approx. 96 percent of their 3500 lb rating. This is also not very good and increases the risk of bent axles. Again, no legal requirements for max. loading.
With ST tires, it is important to observe the rules specific to them - never tow over 65 mph, never tow overloaded and never tow under-inflated. This will help a LOT with preventing a blowout and with maximizing tire life.