I have a light weight
aluminum ATV trailer that I replaced the tires on last summer.
It was the first trailer tire I thought needed a wheel balanced as I could feel the vibration in my PU.
I took it back and found it was an out of round tire. They apologized, replaced the tire and I did not need to have it balanced.
I personally have never felt the need to balance trailer tires. Some people do.
It's like a lot of things involving travel trailers, if it gives you peace of mind and makes your travel more enjoyable, do it.