The other thing that kills ST tires aside from overloading is speed. ST tires are rated for 65mph and running too fast heats them up as much as overloading them does. I would say keep the tires at only 3 years old, as you can usually get 5 years out of a set without too much trouble. However, if the original owner ran them overweight or overspeed, they could be ready to pop. According to the tire experts that post here (we actually have a few posters who have spent their careers in the tire business) damage from overloading and overspeeding is cumulative and irreversible, and generally is not evident just by looking at the tire. If the original owner was not a very good driver, the tires could also have internal damage from curbs, etc. Bottom line, you can't really tell much just by looking at the tires.
I wouldn't replace them for date alone, but I would consider starting with a fresh set if the budget allows. The problem with a blowout is that it can really damage the TT when the tire comes apart, and rip out gas lines, water lines, and wiring in the process. Damage potential varies by mfr, some use sheet metal inside the wheel wells and are careful not to route plumbing and electric too close to the tires, others use plastic wheel well liners with wires and pipes just above and in harm's way. Check your TT when you get a chance and see how it's constructed and how likely you are to suffer damage from a blowout.
Consider adding a TPMS for the TT tires. Many blowouts start as slow leaks, the tire heats up as the pressure drops until it blows. If you can catch the leak with the TPMS it gives you a chance to pull over and fix the problem before the tire self destructs. I use a
Dill TPMS but there are many good systems available.
You can't tell tire pressure just by looking at the tires since they run in pairs on each side of the TT. I rented a dual axle cargo trailer from U-Haul last year to move my daughter back to NJ.

We packed that thing full and decided to check tire pressure before we left. All tires looked fine, but on the right side the front tire was 65psi, the rear was at 0. Had a nail in it. It didn't look flat because the front tire was holding the trailer up, and that front tire surely would have blown from overloading had we ran it down the road like that. (I plugged the tire and all was well.)
E rated tires only buy you capacity if the rim is rated at 80 psi. At 65 psi, an E rated tire is only rated to carry the same weight as the D rated tire. The majority of rims that come with D rated tires are only rated at 65psi, so plan on upgrading rims if you upgrade tires.
I went to 16" LT tires to get away from the 65mph limit and also gain some capacity. Not all trailers have clearance for larger tires however...II had to add a
Correct Track Kit because it gave me the 2" of height that I needed to run LT tires.