This is Feedback Extortion. Do NOT give a partial refund. Respond only "Return for Refund" and do not say anything else. When a buyer is this unpleasant, he will use anything you say against you. Yes, you may have to accept a refund but at least that would get the matter over with. If the buyer is a scammer, the "Return for Refund" statement may get him to back off.
In the meantime, take a deep breath. Step away from the keyboard or IPhone as the case may be. Get a hot cup of tea or coffee or whatever. In a week or so, you will have moved on from here and you will have learned a new skill in dealing with nasty buyers.
I'd also suggest that, if the buyer is correct in saying that you took nearly two weeks to ship, speeding up your shipping process. Slow shipping makes buyers unnecessarily cross, and that is (obviously) something you'd want to avoid in future.
Hopefully your next sale will be a much happier one!
