On several occasions I read or heard expressions like "look you in the eye" (without "at" between the verb and the pronoun). This struck me as incorrect. Yet the same people who use this construct always use "look at" in most other contexts. So perhaps is it just colloquial and not used in formal discourse by convention ? Can the experts clarify ?
I think it's basically an idiom that does not follow the normal rules of grammar.
When "look" -- and "stare" -- are used in a phrase with modifiers, we generally drop the "at". "Look him in the eye", "stare him down", "look it over", etc.
I suppose this might be considered somewhat informal, but I wouldn't be surprised to see it in academic writing, etc.