What source are you getting 応 (ō) from as an affirmative reply? The closest I can find is ōzu (Sinic ō + verbalizing suffix zu; evolving into ōzuru and thence modern ōjiru) as a verb meaning "to reply, to respond; to follow along in accordance with changes; to respond to events; to follow an order or request". The closest sense to "reply" is clearly the first, but that could just as easily be a negative reply. The closest sense to "affirmative yes" is the last, and that one doesn't necessarily have to do with speaking.
There *is* plain-old native Old Japanese おお (ō) that's used as a synonym for はい (hai), i.e. sometimes in a sense of "affirmative yes" and sometimes just as "I hear you, uh-huh". It's also used like "huh" when one just thought of something; or like "hey" when calling after or addressing someone; or like "oh!" as a surprise noise; or like "oh, oh, oooh" as rhythm sounds in poetry or song; or like "ooohhhh" as a groan.