The tires do age and I would be cautious using them if they are that old. The sun and weather conditions age the tires. They are supporting the front end weight of your towed car. I would change them out with new ones at this point. I just bought a tow dolly and have extra tires that came with it in the deal. I wrapped them up and placed them inside my garage out of the elements to keep them as fresh as possible for future use.
Age, usually, as they usually don't get enough miles put on them to wear them out. IMO, if they're ST tires then at around 6 years old, according to the DOT date code on the tire, it's time to look for replacements.
2021 Thor Four Winds 26B on Chevy 4500
I also have EZE-Tow dolly like you. I replaced the original tires after around 10K miles. One tire developed a bubble on one side. I posted a side by side picture of my tires at another forum site (when we had the Class C Forest River). It was suggested that the tires "may have had some sort of radial belt separation", which caused the tire to expand. I was glad we didn't had a blow out. My dolly is kept inside our garage when not in use. So no excessive sun exposure. At 6 years old, I would replace them. Tires are not that expensive. Damage caused by a blow out will be.
2021 Thor ACE 33.1
2015 Forest River Forester 2861DS
2012 Milan Eclipse
I know that my tow dolly tires have the balancing beads inside the tires so no lead weights are required. My tow dolly tires each use 2 ounces of balance beads per tire to correctly balance them. It is based on the size of the tire as to how much in balance beads are needed.