His forehead creases at the statement. What does any of that have to so with anything? He's well aware the man is not his father. His head tilts at the pet comment and he looks confused, before he says, "I'm not a pet. I'm a weapon."

You said so yourself Tony.

Bucky does stand and go back to the food. He's still starving and he hates to waste food. He doesn't say anything one way or another. It's not his decision to make. He doesn't know what New York has to do with anything either but he just stares at Tony while he eats.