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Google offers a Chrome extension called Personal Blacklist. It allows excluding some websites from search results.
I want the opposite. I want to set favorite websites that would pop up in search results first.
Google CSE and site: do this and exclude everything else.
Is there a way just to sort domains, instead of excluding them? Maybe some other search engine? Or, for example, search restricted to Google Bookmarks?
The easy way to search the way you're asking for is to search from Google Bookmarks instead of from Google's home (search) page. On the Google Bookmarks page, you have the same search bar -- any search you make there will only list results found in your Google Bookmarks.
Aside from that, there doesn't seem to be a manual way to sort searches so that specific domains show up first, either in Google or in any other major search engine (Bing, Yahoo!, Ask, etc.).
You can also use the site: filter that you mentioned to filter Google search results to multiple sites of your choosing. For example, you could do something like this as your search query:
javascript site:github.com OR site:gitlab.com OR site:codepen.io
which would search for the term "javascript" but only return results from GitHub, GitLab, or CodePen.
