- "what kind of sites use them?"

Here's a good sample set (AMP posts on Reddit, sorted (roughly) by popularity):

https://old.reddit.com/user/AmputatorBot/?sort=top&t=week

They pop up on reddit fairly frequently. Lot of news sites push them, hard...when people get a share link, especially on mobile, they end up with an amp link. Lot of subreddits have automod rules that delete amp links, and there are bots that look for amp links and reply to the comment with a de-amp'd link.

Commercial blogsites that post often, and specifically focus on 'new' stories that people are searching for online.

Think websites that do news, celebrity gossip, music, games and movies.

Google no longer marks AMP pages in its results, but Bing does.