I'm getting a lot of my social referrals from "weebly" which is not a social media site. Also the number of new users is zero. I'm guessing this is myself.
My question: Why does GA count Weebly as a social site?
Weebly is clearly a web host company. I cannot see a reason for calling it a social media site. It may have some social media elements, but that is not evident. Their site seemed to load too much junk on the home page making it extremely slow so I backed out before it ended. Plus who uses frames anymore? Really.
You are likely getting referrals from a Weebly website. Someone must have linked to your site from a Weebly hosted web site maybe? I do not have the data to know this for sure. I do not know what you mean by the number of new users is zero, but I have to assume that is the GA metric for new users. With GA and how they measure new users, I would not put too much stock into this metric at least not in this case. GA measures users in their own unique way that is contrary to common sense/tradition so I would take some of these metrics with salt when you look at them.
If you are not using a log analyzer, I would install one of the open source free analyzers as soon as possible. You would get alternative and possibly clearer information and may help with any confusion.