I believe, but I may be wrong, that the inconsistency arises from Sunday being the Christian sabbath. That “starts” the week, but it’s a traditional day off for religious observance. And this tradition goes back well before the 40 hour work week, and the common Monday–Friday work week. Which is to say that “weekend” didn’t originally have connotations about which days were work days, they were typically all work days except for the Christian sabbath. Which as a retcon makes the present colloquial usage even odder, even if it’s (maybe?) more consistent with how other countries/cultures use it.