I understand why the answer is vulnerability, but this doesn't really make any sense if you think about it.

How would the successful developments of nuclear weapons leave your country more vulnerable? It's the complete opposite.

First off, when it comes to the GRE, dump the meaning and stick with what the sentence says.

Secondly, when one nation develops nuclear weapons, other nations do so to defend themselves and this increases the possibility of nuclear warfare. Peace is maintained on the basis of fear or Mutually Assured Destruction (MAD), but chances of a nuclear war has gone up manifold.

That’s an interesting point sometimes even well-intended security measures can create new vulnerabilities or tensions. It really comes down to how security is implemented and whether it's done with long-term stability in mind. I was recently reading about this on noblesecuritygroup., and it highlighted how balanced planning is just as important as the tools themselves.