When I click a Facebook like button in Firefox, I see the following behaviour:
It is not happening in Internet Explorer. Is there a popup setting or an add-on I can use to fix this problem?
Weebly has a help page that deals exactly with the "Like" button. The first part of the tutorial walks you through generating the Facebook code to be included in your page. The last step of this part is important, because you have to choose the right type of embedding code—in this case iframe. (I think here is your problem, because the XFBML code doesn't work with Weebly.)
Select the iframe code and copy it. This is important as the XFBML code will not work properly.
Then, the second part of the tutorial presents the steps you need to do to embed the code in your website.
As far as I understand your question, you are asking for a way to integrate facebook like button on all posts dynamically, right ?
You can do that by simply adding this code to your post template
<div class="fb-like" data-href="{Permalink}" data-send="true" data-width="450" data-show-faces="true"></div>
{Permalink} will be dynamically replaced with the post link.
Best Answer
The answer is in Facebook Like button + Firefox + neverending popups.
You have to allow third-party cookies in Firefox. The Facebook like button script laughs at your futile attempt to keep your privacy safe. Yikes!