그저 is a common word similar to "just", "only / solely", or "always / nothing but" depending on the context.
- 그는 하루 종일 그저 잠만 자고 있다: He is just sleeping all day long.
- 그녀는 그저 웃기만 했다: She only smiled saying nothing.
- 비가 그저 내리고 있다: It is raining with no end.
- 그저 바라보기만 하여도: Even if I just look at [her/him/you/?]..
If you go deeper, there are more subtle usages too.
- 요새는 그저 그렇습니다: These days it is so so (nothing remarkable to mention).
- 이 영화는 그저 그래: This movie is just so so.
- 그저 한번 해 본 말이다: I was just saying it (without particular intent).
- 내 그저 그럴 줄 알았지: I knew it would turn out like this (그저 = no wonder / no surprise)
By the way, 그저께 (the day before yesterday) is shortened to 그제, not 그저.
그죠 is short for 그렇죠(isn't it (so)?), and is distinct in pronunciation and intonation.