This is a video of the tires (and their out of round condition) on one of my trailers. The concept of balancing trailer trailers a;ways seem to stir the pot so I thought I'd share my video here.
Back in 2010 I bought a different trailer than the one in the video. It was a flatbed PJ car hauler trailer, which I hauled my Jeep TJ Rubicon on. The tires were so badly unbalanced, the trailer vibrated going down the road empty. I took the tires/wheels to Discount Tire. They said 2 of the 4 were badly out of round, and they saw no point in trying to balance them. I took all 4 tires and wheels back to the dealer I bought the trailer from and the sales guy gave me a "deer in the headlights" look when I said the tires were so badly out of round that they couldn't be balanced. He said "trailer tires don't need to be balanced." I told him they DO need balanced when I can feel the trailer vibrating going down the road when it's empty. They rounded up a new set of tires for me a few days later, I had them balance on the way home, and the trailer towed way better after that.
The trailer in the video vibrated as well. I didn't notice the vibration until I towed it with my Silverado Dually (stiff suspension). I could feel the vibration being transmitted through the trailer hitch to the truck.
Balancing the tires solved the issue on this trailer as well.
https://www.youtube.com/watch?v=CwFMpTrFJHM
On a heavy RV, there's probably a lot less likelihood of feeling a tire balance or out of round condition... but on an empty utility trailer, it was very evident.