I recently had the western blot drawn through quest, had the university send the package to a quest near me, and it took 10 days to get my results back
I have the impression that the WB lab (at the University of Washington) runs the tests once or twice a week. If so, any time beyond 10-14 days probably involves delays in sending the specimen and/or conveying the results from UW to the local lab, and from that lab to the doctor or patient. I agree 3 weeks seems long, but have no first hand experience.