I like the thin size but am concerned that they might curl at the edges. Do I have a legitimate concern here? What is the benefit of the 8mm tile, longer warranty? Or why would it a better or worse choice?

Our 3/8" Sure Fit Rubber Tiles will not curl at the edges. That is the same with all of our rubber tiles. So there is no concern there with that. So why one would choose a 3/8" rubber over an 8mm rubber is due to what they are doing in the gym. If you are using some heavier weights, our 3/8" rubber products will perform better in the long run. When dropping weights, over time, the subfloor can get damaged due to the constant dropping of heavy weights. The thinner the rubber, the sooner this can happen. So if you are going to be dropping weights over 50 lbs on a consistent basis, we would suggest going with our 3/8" rubber tiles and rolls. If not, a thinner rubber is totally fine. The warranty for most of our rubber flooring is 5 years.