Why do we invert word order when asking a question?

What's the difference between an inverted question and a normal-order question? Why invert? Is there a reason or a benefit?

• I love you?
• Do I love you?

Solution 1:

"Do I love you?" is the proper form. In spoken English, though, you can, and in suitable situations you would, use the form "I love you?"

To put this into an example (spoken):

Situation A:

Person A: "This guy came in and asked whether he can borrow my cell phone. Do I know him?"
Person B: "Yes, he's one of our former employees, we've worked together long time ago."

Situation B:

Person A: "Have you heard? Some guy went to the bank today and started shooting people.
Person B: "Yes, it is kind of sad, because he's one of our former employees. You two have worked together long time ago."
Person A: "I know him??"

In situation A, you are really asking the question, because you want to know the answer. In situation B, you kind of already know the answer, but for the matter of the situation, you want to assure yourself, as if to not wanting to believe the result.

Solution 2:

The non-inverted question is used in one specific case: when the first speaker has expressed as fact something the second speaker doubts. @RiMMER's example demonstrates that. Or, to use your sentence:

Person A: Since you love me and I love you, we should get married.
Person B: I love you?

If B had said "Do I love you?", it would be an expression of genuine curiosity; as it is, he's just expressing his uncertainty or disagreement.

Solution 3:

I suppose a benefit of having a different word order for questions is that you can usually tell a question from a statement as soon as the speaker starts asking it.

Can you— (starts a question)

You can— (starts a statement)

I’m not sure this is really helpful, though, as you can generally tell anyway, from body language or tone of voice. Even if this is useful, questions could of course be distinguished in any of a dozen other ways (and I imagine they are, in various other languages).

Generally there are not good well-known reasons for all the quirks in English.