Affirmatives

I don't have much. The Kokugo Dai Jiten quotes for early usage don't date any further back than the late 1700s, while Daijirin doesn't give usage quotes, just usexes; same for Daijisen. None gives any etym.

The etym in the JA WT entry at ja:はい suggests a borrowing either from Cantonese 係／系 (hai6, “yes; it is, there is”) or from Mandarin 拝 (bài, “to kowtow; to worship; to salute; to pay respect”). The Cantonese term could be viewed as similar to other languages' versions of "it is so," while the Mandarin term could be seen perhaps as "I acquiesce, I go along with what you say."

I'm intrigued by how late this borrowing might be, judging from the late date of quotes in the KDJ, and I wonder at how that might have happened -- perhaps something in the popular media helped spread the term? No real idea.