There's an inner lip that somehow gets messed up and gooey out here in the desert. I had the SAME EXACT thing happen to mine just a few months ago. Bought the replacement parts. Pulled out the old weather-strip pieces. Cleaned off the black goo smears with solvent. Installed the new weather strip pieces and it's good as new.
Not sure what it is about these weather strip pieces and the PHX heat. Must just be the right combination of cleaning chemical and heat that turns them into sticky mush. Plus the outer lips were dry-rotted to hell anyway.