Weather stripping

I have inherated a 99 Anniv. Edition Miata and know little about it except its a blast to drive. So anyway I have this heavy weatherstrip over the drivers side window drooping down. Of course I can raise the window to hold it up but who needs that?.It appears that parts of this thing just wrap around the round tubing frame of the top but there is something else that is broken at the middle where it mysteriously attaches in some more permenant way?
Has anyone replaced this stuff? And if so how does it attach? Also wondering if this is considered part of the car or part of the top? Thanks in advance for any answers.....Don

windshield adhesive may be a quick cheap easy fix