No offense as you've probably put a lot of work into it, but, you shouldn't be using iWeb. It is way too outdated to make a modern website that will carry into the future or be mobile friendly without adding code to the pages. The website is not up to modern standards and is getting older day by day.
If you want Google not to downgrade the search results you need to get the site mobile friendly.
What you should end up with is one site for large monitors, and another that it would redirect people to if they are on a mobile device.https://www.google.com/webmasters/tools/mobile-friendly/https://developers.google.com/webmasters/mobile-sites/mobile-seo/common-mistakeshttps://discussions.apple.com/thread/4921113?tstart=0https://www.wix.com/
might be worth looking in to.
For now until you get it up to modern standards at the very least you should standardized the colors on each page, backgrounds, toolbars, etc, and please get rid of the black background pages if nothing else, terrible.
I'm guilty of the same, my site isn't mobile friendly, need to practice what I preach.