Oui, tu le dois! why "le"? and not simply oui tu dois
I think maybe because there is an implied object, as in, "you have to ___", and in English we can get away with not filling in that blank, but in French you need to fill it in with an object, and thus "le" is necessary--maybe! just speculation.
That's a great speculation. I wonder why in another example "Je dois" is correct instead of "Je le dois", though.