With Blogger, you have the advantage of a site which is owned (and favored) by Google. Really, how many Weebly sites do you see ranking on page one for any search term? On the other hand, Blogger blogs almost always rank well, whether they keep the Blogger subdomain or use the blogger's own domain. These blogs are search engine friendly, easy to update (unlike a static site) and provide instant credibility for the new webmaster.
Weebly gives you more design options for the layout. However, Blogger is fast to create and the pages seem to load quicker.