A jukuu.com example sentence for 我吃不了 is:
I don't think I can manage a huge fish like that.
(wǒ kàn wǒ chībuliǎo zhèmedà yītiáoyú)
It makes sense to me to say 我吃不了这么大一条鱼 (which I translate to "I can't finish this big of a fish") without the initial 我看 (wǒkàn). Judging from the translation, 我看 means "I think" in this context, but then I would expect 我想 (wǒxiǎng) or 我觉得, as 我看 ordinarily means "I see..." （e.g. 我看一下).
[NB. The English is non-literal, with "manage" instead of "eat".]
Question： What does 我看 do in the sentence 我看我吃不了这么大一条鱼?