In the current version, 1.3-07u, weaved services are started by cron.
If you run
sudo crontab -l
you can see the commands which are being run (there may be other processes using cron besides weavedstart.sh).
To edit this file, run
sudo crontab -e
Do a search for "linux cron" to learn more about using cron. I believe that you would use this with @reboot.
You might also wish to study the file /usr/bin/remot3it_register which is a batch installer script. After logging in, it will install services automatically. Study the comments in this file for more info.
My guess is that after running weavedinstaller this way, you will want to remove that line from the crontab so that it doesn't run again the next time you reboot. This is an exercise in bash programming.