It is kind of like the situation with gör/does the other day--having "are" there is an english thing. You don't need it in the sentence to express that you're crying right now.

Jag gråter. I'm crying.

Varför gråter du? Why are you crying?

Not that it really answers the "why" but the pattern is simply [question-word] [verb] [subject] [optional other stuff].

I think English is the language that should explain its logic :-). In English the participle of the verb to cry seems to function as an adjective. Compare with Why are you sorry? which translates into Varför är du ledsen? in a straight forward way.

No, not really. This is a question, where the subject and verb change places (which occurs in English too).