OS X has some new security settings that can prevent you from using your favorite application even when they pose no security risk at all.
To fix this you can either;
1) Right click on the application Icon and select Open. Then in the dialog that appears select the Open button.
2) Open up System Preferences and select Security & Privacy. Then where it says Allow apps downloaded from: select Mac App Store and Identified developers
The first option will let you work with EverWeb from now on. The second option is more permanent and will make sure you don't get this error for other applications.