The only place where I can find "File Size" available is through the Design Binder/Design Journal.
The problem then becomes; "How to get information from a journal to a drawing?"
Sry, that's all I got.
The problem with that is often, the file size changes depending on what version of windows you open it on, which version of Solidworks? etc...
Why does that need to be in a drawing? It has nothing to do with the information needed to make the part.
Don't ask me. I just do what I'm told.