I think you need to use Custom Web Publishing for that.
IWP wants to be the parent window.
In case it is helpful for other people who have the same question, I was also in touch with Filemaker Technical Support. Here is what he had to say:
Unfortunately, you cannot use IWP in an iFrame because IWP needs to take control over the whole browser window.
If the FileMaker bit is only a part of your website, you can put a link on the Weebly site to the FileMaker IWP layout and within the FileMaker IWP layout put also the links to come back to the browser by using OpenURL and specifying it to be opened in the same window.