Weebly does allow facebook marketing on their site. You should take a look at their complete Terms of Service, the most important restriction on advertising is:

(q) include more than three ad units per page, or any advertising that greatly reduces the usability of the site.

So, you would need to be careful about how many banners you include. That being said, many of Weebly's templates work really well with affiliate sites. The ability to insert HTML and Javascript files gives you a lot of flexibility.

I've created a couple of demo sites that show how you can use affiliate data feeds on a Weebly site. You can see them here: http://www.webbuildersguide.com/website-builders-reviews/weebly-review/

False advertising, writing glowing reviews of themselves, disregard of existing customers businesses... etc., etc., etc. Do yourself a big favour and switch to Wordpress-- it's not much harder to master and they have many drag and drop templates available. You will thank me later.

Weebly is one of the worse organizations I have ever dealt with.