https://eclecticlight.co/2015/04/18/in- ... en-courbe/With the advent of road construction in the early nineteenth century, a margin of stone became used to segregate pedestrians from vehicles, and that too was termed a curb. Whilst it has retained that original spelling in the US, here in the UK it changed quite quickly into kerb.
It's an interesting article with a lot of in-depth stuff I didn't know. I found a couple of other sources on the subject, but they were too cursory for comfort; this was the best so far. Articles clarifying the history behind differences between British and North American English are usually not hard to find, but the topic of "curb" vs. "kerb" took more work, for some reason.