I believe SEO is fairly complitcated, but for a simple website builder such as Weebly, please outline some techniques for topping the ranks. (Note: Heard from numerous people that Weebly is bad so SEO but am deciding to go with it anyway)
In my experience, choosing a blogging platform has nothing to do with its ranking. Why? Sounds like they are saying that Weebly is taking personally by search engines. That's definitely wrong. I've seen many weebly hosted blogs/sites having a good ranking in Google. So I suggest you to go for it. You just need to have quality works if you want to have better rankings.
Any blogging platform will surely work as long as you will going to do proper SEO in it. Do not forget to update often also. Always put new content since Google always love new updates.