What is it that persists through both metaphysics and physics? What writers have written specifically about the implications of one for the other and vice versa? I understand that they are analogous, but would like to see some of that articulated. If you can do it, DO IT!!
I wouldn’t characterize it as a ‘something’ that persists through both. I’d say instead that at its core, physics begs a metaphysical question, that’s all. The physicist can prove that something exists in a particular way or behaves in a predictable manner, but he or she can’t say definitively what that something actually is.
I think that’s a good start. Let’s see what others have to say about the matter!
This better not be for one of your homework assignments. 
This particular question has just been on my mind for a while. I see that there are parallels between these but I’m looking for good arguments to define their nature. I promise I’m not doing homework. Right now for my class I’m actually reading a guy named Hintikka and some David Lewis. Lots of identity theory and possible worlds stuff. If I ask about possible worlds, that’s homework, but I wont!!
Physics deal with the laws of the universe. Metaphysics deals with the laws of reality. The difference is that metaphysics isn’t based on math, but on reasoning.
It seems metaphysics deals with the ‘meaning’ of raw physical observation.
As physical observation becomes more subtle, metaphysical ideas of meaning become more nuanced and subjective.