Dicker can mean "big guy" in the sense of being overweight, but calling someone "dick" isn't necessarily an insult. It's just the opposite of "dünn" (thin). Calling people "fett" or "dürr" on the other hand has an insulting connotation that "dick" and "dünn" lack.
Another things to consider is that "dicker Freund" doesn't necessarily mean "fat friend", it can also mean "very good friend" in the sense that the friendship between you is thick/strong.