I am assuming you are talking about the WC logs to ~/Library/Logs/WeatherCat that appear to be duplicates of those written to "system.log"? The user logs are deleted after eight days, so they don't use much disk space after that. AFAICK the system.log is rotated daily. I assume that is why
Stu set up WC to save them for about a week.
They are often handy for discovering what may have been causing a problem.
A few of the services that you may be uploading to have checkboxes that enable/disable those entries and the Custom Web (WU & CWOP), Webcam and Misc2 have particular logging choices.
Unfortunately, in Catalina, they are much less available. Apparently you can still search for "WeatherCat" but I'm not sure how easy it may be to search for multiple criteria. Still waiting to
hear from folks using Big Sur to see if Console has been made as useful as it was pre-Catalina.