I'm sorry but again you need to provide the weewx log data, not the os log data (which is not including anything weewx for some reason). There is no mention of weewx in your 'syslog' attachment at all.
Since you seem to be running rsyslog according to one log snippet, you might trying switching to rsyslog for your weewx logging to make finding the log data easier. You can do this via:
sudo cp /etc/weewx/rsyslog.d/weewx.conf /etc/rsyslog.d/weewx.conf
sudo systemctl restart rsyslog
sudo systemctl restart weewx
Then your weewx logs will be in /var/log/weewx/weewx.log and nice and easy to grab. You will probably need to use sudo to read them.
(I tested the above using debian12 so it should work the same on anything 'buntu)