Hi Paolo68,
Sounds like something may have got corrupted. First run Disk Utility over your hard disk (Applications->Utilities->Disk Utility) to make sure there are no issues with the file system.
Next try replacing WeatherCat's preferences file - this can be found at ~/Library/Preferences (where ~ is your home folder). If the Library directory isn't visible use the Finder's Go->Go To Folder menu item and enter ~/Library/Preferences
Find the file called com.trixology.weathercat.plist and rename it to something like com.trixology.weathercat.plist.old then run WeatherCat - it'll create a new preferences file. If it launches, you'll need to set up the options again.
If it doesn't launch, make a copy of the WeatherCatData folder (again found at ~/Library) then double click WeatherCat and immediately hold down the ctrl key - this will cause it to boot to the data restore window. Select the most recent backup then restore it. WeatherCat will quit at the end of the restore. For more info on data restore mode, please see the WeatherCat manual page 51.
Run it again and hopefully it'll launch normally and download the missing data from your logger - if not, try an earlier backup.