The “kerb” in the UK is the step between the road surface and the bit the pedestrians walk on. More properly “kerbstone” I guess.

Something to remember is that not very long ago, many words didn't have an accepted spelling, they were spelled phonetically. Although Curb would sound correct since it might be to curb things on the road from hitting the pavement/sidewalk, spelling it as kerb would have been OK.

Bill Bryson talks about this in one of his books (long time ago, I can't remember which) and it explains weird things like why the US pronounce Derby as it sounds but the Brits call it so it sounds like Darby.

Yes, and they also spell the things on your wheels "tyres"!

"Mind you don't scrape your tyres on the kerb!"

No, we call it a pavement