You're not providing enough information and we unfortunately cannot read minds here....
Did you install with setup.py or apt ?
Which syslog are you looking at ? On a pi you want to look at /var/log/syslog (not /var/log/messages)
You should probably be using "systemctl" for your commands ala "systemctl enable weewx", "systemctl start weewx", "systemctl status weewx". I also found that if you do a lot of starts/stops manually with init.d startup files that systemd can get confused and weewx won't start due to the pid file that can get left around in some cases. Sometimes you need to do multiple stops to clear systemd's brain a bit.
But you are not providing nearly enough info for people to help.