How would you remove adhesive weatherstripping?

It's hard to say, this type of weather stripping is normally installed into a track. The nylon backing is very stiff. I think a type of double stick tape would work best. You might be better off going to a hardware store in your area and see what kind they suggest. Also take a look at our 58-180 self stick-on foam door seal. That might work better to seal up your door. As for removing the old seal, there aren't a lot of tricks for it, at least aside from the usual. Just try to scrape it off as best as you can without damaging the window!