This has several meanings:
1) Somebody who hasn't got the mental capacity to see they are destroying themselves.
2) Somebody with a small penis
3) Somebody who has dreadlocks and a lot of piercings - also see greebo, emo and mosher
Person one: They look there's Hal
Person two: Mm, yeah, he's a right weiney
Person one: In what sense, man?
Person two: In every sense, man.