You should be able to use the tweak if you sign in to Cydia with the account e-mail you used to purchase it with the first time. Cydia is a lot like the App Store in that once you buy a tweak, it's yours to install on new devices.
If you run into any issue with the reinstallation, may I suggest you contact the developer and ask for assistance.
Sorry, but I don't know the status of it (whether it is compatible with iOS 6.1)...
Marilyn