頑張って見るよ
What does this mean? To me, it feels like "Try my best and see".
頑張って見るよ
What does this mean? To me, it feels like "Try my best and see".
(-て)みる is one of the Japanese subsidiary verbs that means "to try V-ing". As a subsidiary verb, the original meaning of "to see" has been lost, at least partly. (Compare how, in English, "have" as in "I have to do" or "go" as in "I'm going to do" has lost its original sense of having or going.) Subsidiary verbs are usually written in hiragana in formal writings, but some people don't pay enough attention to this rule and use kanji anyway.
Note that (-て)みる means "to try V-ing", not "to try to V". See: What is the difference between "verb+て+みる" and "verb+(よ)う+とする"?
So 頑張ってみるよ means "I'll try my best (anyway, and see what happens)". 頑張るよ just means "I'll do my best", and てみる adds the implication that the speaker is not sure about the result.
In non-typical contexts, 見る can be taken literally; "I'll try hard and watch it (e.g., the TV program broadcast at 3 a.m.)". Check the previous context.
I don't think it's written with a kanji on みる for those cases.
Nevertheless, てみる means "to try to ". It can be both capability (see if you can do it), or invitational (Just give it a shot to see how it's like).