Weebly Site I Created Here.
I can see why Weebly would be appealing to people. It has a very interesting interface, especially if you have been using one of the others for quite a while. You basically just drag parts onto your page and then you align them and re-size them pretty easily. I noted in the single entry that I put on my Weebly Blog that an adventurous person could very easily make it look like an online magazine. Weebly does lack the sheer numbers that WordPress boasts, and the seamless integration into Google+ that Blogger has, which may put a lot of people off, but my advice if you do go and try out a Weebly blog (or you already have one) is to spend a day getting a great template in order. If you get your Weebly Page to look more like a flowing business, news, or general information site, then you can take advantage of the "I don't like bloggers" crowd, who would read a blog if they thought it was a news site. Yes there is one of those crowds out there.
Another interesting thing about Weebly is it does seem to have integration features that WordPress seems to lack. Have blogs on other blogging formats? No problem, you can very easily set up an RSS feed to your other blogs and make it look like they are just part of your normal Weebly Page. They seemed to at some time or another realize that they have some catching up to do, and decided to make it easier on multi site bloggers instead of more difficult. I haven't played around with it much, but may somewhere down the road. The important thing for people to know is that it is there just in case you worry about "another place to blog" when in reality you can just make it a standardized place to share your blogs.
All in all Weebly is well worth trying and well worth sticking with if it is where you are now. I would suggest perhaps trying the RSS integration and maybe getting a Blogger Blog on the side, just because of the Google+ integration angle. It would help to draw people in to your Weebly Site and it couldn't hurt anyway, to have fall back positions.