I found your website in older support questions. There seem to be two issues on your site:
1. Social Login
Social Login sets avatars for users that have logged in via Social Login. Unfortunately, when it does this, it strips the user id from the image, so there's no way for BP Hovercards to find out to which user the avatar belongs. In short, for now unfortunately no hovercards for users logged in with Social Login.
2. BuddyPress Social
Users that didn't login or signup to your website with Social Login (like yourself) do get a hovercard. But because BP Social uses the same script (tipsy) to display popups, it includes some styles that interfere with the hovercards. Try adding another rule for .tipsy .tipsy-inner that sets max-width back to 350px (instead of the 200px of BP Social).