If you check out this piece, one of the characteristics or properties of every entity mentioned, is that it exists. You can further identify that if a rock was thrown, it moves through the air. The motion exists. When you weigh the rock, it’s specific weight exists, and so on.
[my bold]
In his podcast, Episode 10 — March 10, 2008, Dr. Peikoff responded to the question:
05:14 : [A metaphysical question.] “‘What is existence? Existence is an attribute possessed by existence, and we directly perceive existence.’ (…) ‘The fact that I can’t define “existence” bothers me. Is “existence” then kind of a misleading concept?’”
His response to the first part is especially relevant to what you have said, that existence is a characteristic or property [an attribute] of everything that exists.
You can listen to his reply to that question on his website directly here.