I've had good SERP results with a Weebly site. Another Weebly site has not done as well. The latter, I put a domain on it. I have it set up within Weebly such that mysite.com is the site name instead of mysite.weebly.com. Do you think that matters? Would it do better if, like the first one, it was mysite.weebly.com? In other words, by using my own domain name, do I get any bump up for the authority of Weebly?