Nah, Omega first appeared in FFV I believe (although I never finished FF3j, so I may be wrong), and a "Weapon" has since appeared in every FF game to date, besides FF9. Atma (which is often believed to be a translation of "Ultima", though he was, admittedly, hardly a "super boss") appeared in FF6, and Ultima was featured in 7, 8, and 10, while Omega also appeared in both 8 and 10.

Squaresoft and the Final Fantasy series is notorious for its games heavily referencing each other, as well as the references to other sources, from religous and mythological references to referencing movies (ie. Star Wars).

The Weapon thing is one of those trademarks - one of those things the games often have in common with each other.

To your credit, though, I have read many, many theories that try to prove that every FF game ever released, or at least the majority of them, can all be covered under one, large universe. Whether it's true or not, you sure do have a good imagination.