It seems to me that Weebly has a long term strategy. They are trying to build a good user base. As they improve their service those non-technical users will learn how to build more complex websites and eventually some applications.
It is sort of like starting a Kinder_garden with the goals of adding a Grade each year so your students won't have to look for another school.
That doesn't have anything to do with them making money. I don't think their monetization path is very important because best-in-breed web applications don't have a problem getting acquired.
If Weebly was a Web 1.0 company, the founders would be billionaires already.