Yo no tengo mucha idea aun asi miro el log, asi se aprende (creo).
En el Weewx.logLo que veo a inicio es un retraso en el reloj que ya vi en otros errores de este post, creo que a burgati, mirate su post
Dec 29 19:20:53 raspberrypi weewx[629]: engine: Clock error is -17.15 seconds (positive is fast)
Aqui por alguna razón se intento añadir un registro mas a la BBDD
Dec 29 19:27:10 raspberrypi weewx[629]: manager: added record 2016-12-18 11:20:00 UTC (1482060000) to database 'weewx.sdb'
Dec 29 19:27:10 raspberrypi weewx[629]: manager: added record 2016-12-18 11:20:00 UTC (1482060000) to daily summary in 'weewx.sdb'
Dec 29 19:27:10 raspberrypi weewx[629]: manager: unable to add record 2016-12-18 11:20:00 UTC (1482060000) to database 'weewx.sdb': UNIQUE constraint failed: archive.dateTime
y al final te quedaste sin hora
Jan 1 00:00:36 raspberrypi weewx[362]: Starting weewx weather system: weewx.
Jan 1 00:01:36 raspberrypi weewx[538]: engine: waiting for sane time. current time is 1970-01-01 00:01:36 UTC (96)
Jan 1 00:02:36 raspberrypi weewx[538]: engine: waiting for sane time. current time is 1970-01-01 00:02:36 UTC (156)
Jan 1 00:03:36 raspberrypi weewx[538]: engine: waiting for sane time. current time is 1970-01-01 00:03:36 UTC (216)
Jan 1 00:04:36 raspberrypi weewx[538]: engine: waiting for sane time. current time is 1970-01-01 00:04:36 UTC (276)
Jan 1 00:05:36 raspberrypi weewx[538]: engine: waiting for sane time. current time is 1970-01-01 00:05:36 UTC (336)
has reiniciado la PI varias veces a ver si coge la hora?
En cuanto al registro de mas creo que deberás borrarlo de la BBDD
Sys.logEste no se ni por donde cogerlo, creo que hay un baile de fechas en el, pero no se, no te fies mucho de mi...
Dec 30 09:52:48 raspberrypi systemd[620]: Time has been changed
Dec 30 09:52:48 raspberrypi systemd[1]: Time has been changed
Dec 30 09:52:48 raspberrypi dbus[370]: [system] Successfully activated service 'org.freedesktop.UDisks2'
Dec 30 09:52:48 raspberrypi systemd[1]: Started Disk Manager.
Dec 30 09:52:48 raspberrypi udisksd[876]: Acquired the name org.freedesktop.UDisks2 on the system message bus
Dec 30 09:52:49 raspberrypi dbus[370]: [system] Activating via systemd: service name='org.bluez' unit='dbus-org.bluez.service'
Dec 30 09:52:49 raspberrypi systemd[1]: Starting Bluetooth service...
Dec 30 09:52:49 raspberrypi bluetoothd[887]: Bluetooth daemon 5.23
Dec 30 09:52:49 raspberrypi dbus[370]: [system] Successfully activated service 'org.bluez'
Dec 30 09:52:49 raspberrypi systemd[1]: Started Bluetooth service.
Dec 30 09:52:49 raspberrypi bluetoothd[887]: Starting SDP server
Dec 30 09:52:49 raspberrypi kernel: [ 54.753626] Bluetooth: Core ver 2.21
Dec 30 09:52:49 raspberrypi kernel: [ 54.753957] NET: Registered protocol family 31
Dec 30 09:52:49 raspberrypi kernel: [ 54.753980] Bluetooth: HCI device and connection manager initialized
Dec 30 09:52:49 raspberrypi kernel: [ 54.754023] Bluetooth: HCI socket layer initialized
Dec 30 09:52:49 raspberrypi kernel: [ 54.754053] Bluetooth: L2CAP socket layer initialized
Dec 30 09:52:49 raspberrypi kernel: [ 54.754114] Bluetooth: SCO socket layer initialized
Dec 30 09:52:50 raspberrypi kernel: [ 54.911079] Bluetooth: BNEP (Ethernet Emulation) ver 1.3
Dec 30 09:52:50 raspberrypi kernel: [ 54.911119] Bluetooth: BNEP filters: protocol multicast
Dec 30 09:52:50 raspberrypi kernel: [ 54.911167] Bluetooth: BNEP socket layer initialized
Dec 30 09:52:50 raspberrypi dbus[370]: [system] Activating via systemd: service name='org.freedesktop.hostname1' unit='dbus-org.freedesktop.hostname1.service'
Dec 30 09:52:50 raspberrypi bluetoothd[887]: Bluetooth management interface 1.10 initialized
Dec 30 09:52:50 raspberrypi systemd[1]: Starting Hostname Service...
Dec 30 09:52:50 raspberrypi pulseaudio[871]: org.bluez.Manager.GetProperties() failed: org.freedesktop.DBus.Error.UnknownMethod: Method "GetProperties" with signature "" on interface "org.bluez.Manager" doesn't exist
Dec 30 09:52:50 raspberrypi pulseaudio[871]: org.bluez.Manager.GetProperties() failed: org.freedesktop.DBus.Error.UnknownMethod: Method "GetProperties" with signature "" on interface "org.bluez.Manager" doesn't exist
Dec 30 09:52:50 raspberrypi systemd-hostnamed[917]: Warning: nss-myhostname is not installed. Changing the local hostname might make it unresolveable. Please install nss-myhostname!
Dec 30 09:52:50 raspberrypi dbus[370]: [system] Successfully activated service 'org.freedesktop.hostname1'
Dec 30 09:52:52 raspberrypi org.gtk.Private.AfcVolumeMonitor[788]: Volume monitor alive
Dec 30 09:52:52 raspberrypi systemd[1]: Started Hostname Service.
Dec 30 10:07:07 raspberrypi systemd[1]: Starting Cleanup of Temporary Directories...
Dec 30 10:07:07 raspberrypi systemd[1]: Started Cleanup of Temporary Directories.
Dec 30 10:09:01 raspberrypi CRON[6812]: (root) CMD ( [ -x /usr/lib/php5/sessionclean ] && /usr/lib/php5/sessionclean)
Sep 23 04:03:42 raspberrypi dphys-swapfile[372]: done.
Dec 29 18:41:09 raspberrypi systemd[1]: Started LSB: Autogenerate and use a swap file.
Dec 29 19:17:25 raspberrypi systemd[1]: Started System Logging Service.
Jan 1 00:00:27 raspberrypi rsyslogd: [origin software="rsyslogd" swVersion="8.4.2" x-pid="400" x-info="
http://www.rsyslog.com"] start
Dec 29 19:39:01 raspberrypi CRON[7478]: (root) CMD ( [ -x /usr/lib/php5/sessionclean ] && /usr/lib/php5/sessionclean)
Jan 1 00:00:28 raspberrypi rsyslogd: [origin software="rsyslogd" swVersion="8.4.2" x-pid="400" x-info="
http://www.rsyslog.com"] start
Miraria si se ha cambiado algo de fecha en raspi.config...
No te he ayudado mucho lo siento, nos servirá para aprender los dos. Suerte