看 means to look at or watch. 我 看 电视。 The ending -着 is like -ing in English -- it shows a state of being or continuing action. (Contrast this with 了 that shows completed action.) 他 看着 我。 He was/is watching me.

看看 is more casual I think. "给我看看" Let me have a look vs "我看电视" I watch tv.

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看 = to look, 看着 = is looking