I don't know how can they compete with Google on this. They have to offer their product for free. They can't place ads on user's pages, because Google does not require this. Google makes money off the users that do put ads, but this is only because they are the ad network too. Weebly can't make money off them.
I just can't see how Weebly can win. In theory they could get so much better than Google that Google (or Yahoo or Microsoft) buys them because of their loyal user base and better product. This is pretty much the Youtube story, but Youtube at least had the potential to monetize without Google, which is not the case with Weebly.