I had rather edited my previous post, but the option was not active
It should be written 'tate quieta (with the apostrophe accounting for the non-pronounced es syllable). There's no question about it. 'tate is a short form for est?te. I guess the reflexive te is used here because otherwise the verb would sound strange in the imperative: est?! It sounds more as if you were telling your interlocutor: "?Ves esa ni?a que est? sentada? Est? quieta; no como aquellas que corren de aqu? para all? y no paran de gritar". Adding te makes it clear that you're giving an order to the second person, although I can imagine that when it started to be used (don't ask me how many centuries ago) this expression was confusing.
This is the only verb in Spanish I can think of which has stress on the last syllable in its imperative conjugation.
