Lucille: Whoever's behind this whole thing has his connections right in the department. Any leads?
Marv: One guy I talked to told me it was Roark running the show.
Lucille: Whoever it is, he knew I was checking out that hooker almost before I did.
Marv: What hooker?
Lucille: The one you've been obsessing over. The dead one. Goldie.
-- Sin City 2005
I don't quite understand these two sentences with the bold words.
Does did refer to "check out" or "know"? What does the sentence mean?
Why is obsessing over being used here? I think it should be you've been obsessed with/by.
According to the dictionary, obsess over means worry about something all the time. I don't think it applies here.