Substituting "do" after modals

Occasionally I hear native English speakers, typically those from outside the U.S., say things like:

Are you going to the concert this weekend?
Yeah, I might do.

That is, rather than saying I might go or just I might, substituting do for the verb when it'd otherwise be repeated or omitted after a modal. What's this called, how standard is it, and is it newer or older than the other forms? I just don't know how to search for something like this.

The generic term for do standing in for a verb phrase is pro-form do or proform do. I'm not sure if there is technical term for when the do follows a modal verb, but I've seen it referred to as British do.

Your example sounds entirely natural to me. (Yeah, I might do.) That sort of construction (modal + pro-form do) is common in British English, but I gather it sounds weird to American ears.

Regarding how old it is, Merriam-Webster's Concise Dictionary of English Usage says, "These are not recent idioms; they have been under attack and examination at least since Corbett 1823."

I'm afraid I don't know what this specific informal use of do is called. The regular use of do as a substitute, in "do I?" and "I do not", is I believe called do-support.

I think your case is similar to "could you give her this document too?" — "will do", which does sound American to my ears, perhaps southern U.S. or something.

What might also be relevant is why we omit some words but not others in ellipsis, and how we make our choice: to "are you coming to the party?, we could answer simply "no", or "no, I'm not", or "no, I am not coming". Or even "I might", "I might come" etc.

My guess would be that this usage of "might do" and "will do" is not old, though I am not sure.

Modals have always differed from ordinary verbs in Germanic, and in the course of the history of English, they have diverged from verbs even further, to the point where they now belong to a syntactic category of their own.1

The following question was also about do-support, but not specifically about your case: English questions and negation with *do* in syntax