Nominal difference in weight. Almost indetectable difference in the softness of the ride. The thinner middle section "stretches" a bit more and the wheel will be a tad less harsh but just a very little bit. Trade off is strength but that only critical for big people. Even my clydesdale Bubba rides double-butted. Surprised the shop had single-butted.

My road wheels are typically double-butted 15/16 at most. Lighter riders on the road can use this. Our tandem wheels are 13/14s and single-butted.