You can just use this thread, not the second similar thread you opened that had no debug info.
Start with 'weectl extension list' and verify it's indeed there. Sounds like you perhaps (perhaps) have more than one installation there and you're not running the one you think you're running. Try "journalctl -xe | grep weewx | more" perhaps to see weewx log entries.
You should see something like the following in the logs:
Sep 26 11:56:53 pi5 systemd[1]: Started we...@ecowitt.service - WeeWX ecowitt.
░░ Subject: A start job for unit we...@ecowitt.service has finished successfully
░░ A start job for unit we...@ecowitt.service has finished successfully.
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Initializing weewxd-ecowitt version 5.1.0
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Command line: /home/pi/weewx-venv/lib/python3.11/site-packages/weewxd.py --log-label weewxd-ecowitt /home/pi/weewx-data/ecowitt.con
f
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Using Python: 3.11.2 (main, Apr 28 2025, 14:11:48) [GCC 12.2.0]
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Located at: /home/pi/weewx-venv/bin/python3.11
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Platform: Linux-6.12.25+rpt-rpi-2712-aarch64-with-glibc2.36
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Locale: 'en_US.UTF-8'
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Entry path: /home/pi/weewx-venv/lib/python3.11/site-packages/weewxd.py
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: WEEWX_ROOT: /home/pi/weewx-data
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Config file: /home/pi/weewx-data/ecowitt.conf
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: User module: /home/pi/weewx-data/bin/user
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Debug: 0
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: User: pi
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Group: pi
Sep 26 11:56:53 pi5 weewxd-ecowitt[2250251]: INFO __main__: Groups: adm dialout cdrom sudo audio video plugdev games users input render netdev docker gpio i2c spi pi
So for my case above, I'm running a venv/pip installation as user pi and the User modules are in /home/pi/weewx-data/bin/user. If you're running a debian installation your answer will differ, but it'll tell you where the belchertown.py file should be located if you installed it completely/correctly. Yours probably points to /etc/weewx/bin/user