What does 我看 do in the sentence 我看我吃不了这么大一条鱼?
From Collins, you can find this:


  
  (= 认为) think (pt, pp thought)
  ⇒ 看成 (kànchéng) consider
  ⇒ 你看这事儿怎么办？ (Nǐ kàn zhèshìr zěnme bàn?) What do you think we should do about this?
  


The structure of the second example is the same as your sentence.

It is a common usage of "看". But perhaps only used after "我", "你", "你们", "您". But not after "他", a name, a noun, etc.

Edit:
The comment reminds that when used in "怎么看", it can be used with "他" or others, like in "这事他怎么看" (How does he think of this)