Origins and meaning of "can you not"

I don't see why OP should think we need to find an 'origin' for such a standard construction.

Increasingly, people avoid using a negating not at the end of a sentence, as shown by this NGram, but I wouldn't go so far as to call the usage 'archaic'. A little 'dated', or 'formal', perhaps, since the modern style is generally more informal. People are more likely to say/write "Can't you" today, but it really is just a matter of style.

In addition to FumbleFingers' answer, there's the more sarcastic meaning of "can you not": that is, "please don't", as in, "Can you not play the piano so loud in the middle of the night?". In fact, this is how I parsed your question until I read the other answer (needless to say, I was surprised to apparently learn that Sense and Sensibility had such a hip style). I don't know how this version came to be, except through the usual method of sarcastically twisting a very weak statement, literally meaning "Do you potentially have the capability not to...", into a strong one.

In the documentary Terms And Conditions May Apply, Mark Zuckerberg asks the documenters if they are recording him, they say yes, and mark replies with "Could you not?". I believe the use of this word is ironically a subtle protest against personal information being given to big-brother and sold to marketers by internet bohemeths such as Facebook.