Leaking side window seals after windshield replacement

[cmb]

I recently had my windshield replaced by Safelite. The windshield installation itself looks fine, but the weatherstrip at the front edge of the side windows now leaks when it rains. I'd prefer to fix this myself and possibly learn something (instead of bringing it back to Safelite and risk wasting time.)

They replaced the front roof weatherstrip, which is the same piece as the seals along the A pillar. When the door glass closes against this new seal, it seems to be just barely touching it, rather than putting it under compression. As a result, water will creep through and pool on the seats and door sills.

It almost looks as though the channel that holds the weatherstrip should be moved out away from the pillar, closer to where the door glass is when the door is closed. I did notice that the new seal isn't glued to the inside of the channel; it's just held in place by the metal edges.

Has anyone had to solve a problem like this? I usually don't drive my car in the rain, but I certainly want to have the option.

--Colin