Why does Israel get to keep its nuclear weapons?

[drone]

So if you haven't signed, you can make them? And no one bats an eye? Let's say that the newly made independent republic of Durkastan decides to make them right now. Nothing official of course, but it's known. Will anyone even act? What's the point in making the other signees not proliferate the nukes if Joe TinPott can make them?

I wouldn't say "no one bats an eye", but it does depend on the geopolitical situation of the time. North Korea pulled out and built weapons, but they were protected by China and have a gun pointed at Seoul's head, so nothing happened. Look at the diplomatic wranglings that went on when India and Pakistan armed up.

If the new People's Republic of Durkastan wants nukes, they can make them. However, the treaty forbids signatories from exchanging knowledge and material with non-signatories, so Durkastan will need to do the research, build reactors and enrichment facilities, mine it's own uranium, and pretty much start from scratch which costs an enormous amount of time and money.