"커버린" is from 커 버리다, where 커(크다) means "grow big" and "버리다" is an auxiliary verb for "completely".
버리다 is like "up" or "out" in English (but stronger), and means doing something all the way and irrevocably.
- 돈을 다 써 버렸다: I used up all the money.
- 그림을 망쳐 버렸어: I botched up the drawing.
- 나 죽어 버릴 거야: I'm going to kill myself.
- 가 버린 사람: One who's gone for good.
- 잊다, 잊어버리다(forget completely)
- 잃다, 잃어버리다(lose forever).
(잊어버리다, 잃어버리다 have become new words in themselves, so there's no space before 버리다)
So, 커 버린 may be translated as "who has grown up big".
혼자된 나무처럼 ("혼자되" must be a typo)
누군가의 세상을 봐
* 외로워 지친 could have been 외로워 지쳐 버린 too - but it will make 버린 appear twice which is not good.
I see someone's world
Weary from solitude
Like a kid grown up big
Like a tree all by itself