Funkade för mig;
1) Close all Apps that are running
2) Open Cydia, press "Manage" along the bottom and then select "Packages"
3) Select AppSync from the list
4) Click "Modify" at the top right corner
5) Then select "Remove" from the pop up menu then press "Confirm" - This will now remove AppSync.
For the next part you will need either iFile (on the device can be installed via Cydia), i-FunBox (on your computer) or iExplorer (again on your desktop)
6) Using one of the above tools navigate to /var/mobile/Library/Caches
7) Locate com.apple.mobile.installation.plist and delete the file
8) Locate com.apple.LaunchServices-045.csstore and delete the file
9) Now Reboot your device
10) Upon device reboot you may notice that some of you app icons are missing don't be alarmed this is normal it can take a few moments for them to recache and fall back onto the SpringBoard.
11) Once all your apps have re appeared you can open the weather app as normal
Now getting AppSync back on so you can install your Apps
12) Open Cydia, press "Manage" along the bottom and then select "Sources"
13) If you haven't already add our repo - repo.insanelyi.com - if you already have the repo just open it
14) Select AppSync for iOS 5.0+ and install.
15) You can now check that the Weather app is still working which it will be and carry on with installing your cracked apps