The weatherstripping doesn't really stop water, it only slows it down. The silicone holding the windshield does. If the stripping is dry-rotted, probably should be replaced, as it could allow more water than normal to get in there, and might sit accelerating corrosion...
Any reputable auto glass shop like Henderson, Harmon, Safelite, or Belle Tire (they have auto glass now) etc... will have that or an adequate replacement stripping that they can replace it with.
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