Use the direct graph link: https://graph.facebook.com/[User_ID]/picture?type=large . This usually provides an image about 200px wide.
Sites like PeekViewer or various "ID grabbers" require users to paste a profile URL to retrieve the high-res source image from the backend cache. Privacy and Ethics facebook full link size profile picture viewer
Hover over the image to see the link in the bottom right. Use the direct graph link: https://graph
https://graph.facebook.com/USER_ID/picture?type=normal&width=5000&height=5000 facebook full link size profile picture viewer
You can sometimes force a larger size by appending ?type=large or ?width=2000&height=2000 to the image's source link, though Facebook's Graph API frequently updates these permissions. How to get full-size profile picture in Facebook's PHP SDK?
When a user locks their profile, non-friends can only see a low-resolution thumbnail.