Web developers and designers have a tendency to be egocentric about this sort of stuff. We say stuff to ourselves like "How can anybody use this crappy product? You mean like IE over Chrome or Firefox?". The answer is if you don't know any better?.....
To answer your question you need consider the following:
1. Ease of use can be more important that exquisite design - Average person does not value design as much as other things such as ease of use.
$0 site that is easy to build/update and done in hours/days > $$$ for beautifully designed by some flaky web designer/developer that takes 4 months to go live
2. Weebly's Design isn't that bad considering how flexible and forgiving the product has to be.
3. Please show me an example of a comparable product to Weebly that is as easy to use and get live but is significantly better designed?
If such a product exists then the answer might be marketing. Rob Walling of Startups for the Rest of Us Market > Marketing > Design > Product (functionality)
It's sad as a developer to see that Design and Functionality come after market/marketing. It also seems to contradict a bit of my point about ease of use for non techies being a reason for Weebly's success, but if they market well, and it's free then they have a huge leg up.
Really considering what it is Weebly aint too shabby. It's also amazing how many crappy sites there are out there that people continue to utilize. I did some cold calls for my startup idea and I thought the people with crappy sites would certainly get on board, but it didn't quite work out that way.