By "rightfully" do you mean legally? Justly? Equitably? Legitimately? Morally? If you mean legally, then you have described the death penalty, both state and federal. Those representatives can pass legislation imposing the death penalty for "whatever reason they make up." That's why our representative democracy, guarding against absolutism, contains checks and balances. The legislature may pass a death penalty statute, but can they get the executive to sign it into law? Or override the executive's veto? Or will it meet the test of the judicial process? If all of those occur, it becomes law and will be enforced. Thirty-eight states, mine among them, have death penalty statutes for "reason(s) they make up." There is a federal death penalty statute also.
OK,,,,I'LL,,,,GO,,,REAL,,,SLOW,,,FOR,,,,YOU.
Is it your belief that it would be right, morally (if you understand the concept), for legislation to kill you for being fat, or skinny, or for having the bizarre beliefs you have?
I don't expect a direct answer because of your track record. The truth is you think that the majority can rightfully do whatever they want. It's called ochlocracy, and you subscribe to it.