Hovering the mouse near the "edited" area will cause the user card to pop up.
Edit: added the "support" tag because if it's by-design I'd prefer the user card to stay hidden.
The behavior has been changed such that only the avatar triggers the pop-up. As a consequence, the edit link no longer triggers a pop-up. Read up below if you're curious why it used to happen, though. ♪
The linked question demonstrates exactly the same, but I wouldn't call it a duplicate since it doesn't explain why. So I'll do that. ♪
The big usercard only shows up whenever you're hovering over the small usercard on the page. On a question page, your usercard is the following block:
The following is not your full usercard, because it lacks the post timestamp.
The expanded block shows up whenever you're hovering over any point of the usercard. This includes the gravatar, the reputation, the badges, the name, and the timestamp (be it asker, answerer, or editor), but also all that extra space to the right of them. You can see it by hovering over the empty space on, say, my editor timestamp that is above my bronze badge count, that'll trigger the expanded usercard the same.
I can agree that it's not the most comfortable of arrangements, though thankfully we render the card beneath the link so that you can still click it to see the revisions.
Accept rate isn't on the usercard, in case anyone is curious on that. It's printed beneath it, in the scenario that accept rate is visible. For example, if you check on, say, Eric Lippert, who currently only has 2 questions, then you'll note that the card is the full height depicted in the above image of a full usercard. As such, it's not a part of the usercard so it does not trigger expansion.