To "look over" means to examine something. You're right: the two parts are almost contradictory. The "look" part suggests that it is NOT a careful, detailed reading, just a "look." But the "over" part means that whether or not you examined it in detail, you did at least look at all of it. "Could you take a look at this contract?" "I don't have time to look it over right now. But I can give it a quick look. Hmmm... I see a red flag in paragraph 6. I can tell you now: don't sign it until they change the language there. Tomorrow I can look over the rest of it." There's an interesting contrast between the word "look over," which suggests inspecting an examining something, and "overlook," which means to FAIL to notice something. "Thank you for looking over that contract. I had overlooked the problem in paragraph 6." Imagine a class assignment to read Chapter 9 of a textbook. You don't have time to read every word of it. So you read the first sentence of every paragraph in the chapter and look at all the figures and read the captions. You haven't read it, but at least you have looked it over.

to “look over” is to just to examine and process something. For example, while you’re ordering something at a restaurant you can “ look over” the drink menu while also thinking about what you’ll order to eat. Or to “look over” is to consider an option when deciding over multiple options. “We looked over the house today, and decided we didn’t like it.” Hope that helps

I agree with Logan's answer. The verb "to look something over" requires further explanation (an adverb, another phrase like "in detail", or context) to establish whether it is an in-depth examination or just a brief glance. In response to the second part of your question: phrasal verbs are constructed from a verb plus an adverb or preposition (or both), together they form a unit of meaning which is not the same as the separate parts. Also, just like ordinary verbs, phrasal verbs can have more than one meaning. Sometimes we can guess at the reasons why we use a particular adverb or preposition, but sometimes it makes no sense whatsoever. Most English speakers never consider the logic (or absence of logic) in phrasal verbs, and so we normally advise learners to not try to use logic, but just learn the meanings by using context or learning the non-phrasal verb equivalent. So, I wouldn't worry about the meaning of "over" in isolation. That said, I think your suggestions that "over" the second part of "to look something over" might have some deep connection to our eyes being physically above AND seeing to the finish are potentially both correct