Does the size of the Referrer Log continue to grow or is it capped, limited, rolling, etc?

All I want to know is, do I have to keep manually deleting it?

Right now it's not capped. If your limited in your db size then right now you'd need to manually purge it, otherwise even if it's very large it won't cause any issues. We'll get an auto-prune option for this in an upcoming version.

Will there also be a disable option? I would like to turn off the referrer logging.

(No disrespect to your hard work intended.)