Etymology of "had better"

I'm hesitant to answer but what follows is too long for a comment. I shall try to back it up with references if I can find any.

Firstly, I see "hadn't ought" as substandard in the sense that the "had" is superfluous.

You can say, "You ought not to do that" or "You oughtn't to do that."

Secondly I see "had better" as a back-formation from "would better" via "You'd better".

"You'd" is a valid abbreviation of both "you had" and "you would".

I personally find it difficult to give a convincing analysis of "You had better" because it simply doesn't make sense.

On the other hand "You would better" and "You would best" do make sense in that they are describing a hypothetical future action or state.