This was a question at the last Website 101 workshop: How do free services like Weebly and MailChimp make money?
Here’s an article about MailChimp:
It turns out that MailChimp was a paid service first, and figured out how to make money from their program, and only then created a free version. The free version promotes the paid version.
The article mentions a rule of thumb: For every 10 free users, you get one paid user. MailChimp had 450,000 users in 2010, so about 45,000 should be paid users. Rates run from $10 to $240 a month, depending on the number of subscribers.
Here’s an article about Weebly, and how it makes money.
In this model, the Weebly developers make money from their “Pro” users and by making it easy to add Google AdSense advertising widgets.