To me it comes down to what you do on that weekly script …
I actually run a script on a daily basis, however it checks the current certificate to see how long it’s still valid for, and if less than 28 days, will try and renew cert (if more than 28 days left, it exits without doing anything further).
So running on a daily / weekly basis isn’t an issue at all ( as it’s mostly checking).
If for any reason the “renew” fails, then I have plenty more opportunities to renew the certificate before it expires ( and of course it will try and do so every day when less than 28 days to go, until it suceeds ).
Actually renewing the certificate and getting a new one every week strikes me as slightly pointless, adds extra server loads ( for LE) if everyone were to do it, and leaves you in danger of hitting rate limits. For example with current rate limits, and several subdomains on some of my domains ( with separate certs). I’d hit domain and server IP rates if I updated all certificates on a weekly basis.