iOS5: Notification Center

Why doesn't Week Calendar show in the Notification Center?

The Notification Center is for missed/recent notifications, not for lists of data, such as upcoming calendar events.
3rd party apps, such as Week Calendar, cannot show anything besides popup alerts in the iOS Notification Center.

But the Native Calendar shows up?

Yes. Apple apps are granted special powers that non-Apple apps are not allowed to do. This is something technically not feasible on iOS5 for non-Apple apps.

If you would like to see this changed, please leave Apple feedback: here: http://www.apple.com/feedback/iphone.html.