Windshield Weather Stripping - Bottom

Has anyone got a good solution for this? Both 97 vans I have owned have had this problem. The weather stripping between the wiper cowling and the windhsield is coming loose. I simply removed the trim from my (now deceased) old van and found that it started getting some belt squeaking on rainy days. Since we do not have a carport, I thought this was due to moisture getting under the cowling...

I'm thinking of removing the cowling and glueing the weather stripping back on. Or, getting some black caulking and using that in place of the weather stripping.

Thoughts or suggestions appreciated.