patrick,
i would get rid of your old init.d and unit files. then the new units that came with v5 will just work.
something like this (make copies of the files before you rm, if you like):
sudo update-rc.d weewx-multi remove
sudo rm -f /etc/init.d/weewx-multi
sudo rm -f /etc/default/weewx-multi (do not delete /etc/default/weewx)
sudo rm /etc/systemd/system/weewx*
be sure that the values in /etc/default/weewx are correct. for a systemd install, this is all you need:
WEEWX_PYTHON=python3
WEEWX_BINDIR=/usr/share/weewx
other entries that you might have there are used by the sysv script. the systemd units are hard-coded (because systemd environment handling and too many systemd changes to bother tracking), so /etc/default/weewx is used only to fill in the entry point stubs /usr/bin/weewxd and /usr/bin/weectl
then, since you are using systemd, you can just follow the instructions on the wiki: