Ah, the ambiguous "why" of motivation: my old enemy, we meet again!
My job often requires of me that I ask people what their hypotheses are for third parties' behaviors. I have to be very, very, very careful how I phrase such questions, because, as you have noticed, the question "Why do you think he is crying?" can be parsed two very different ways:
"What do you think his reason is for crying?"
"What are your reasons for thinking he is crying?"
The second of these two questions – especially when phrased using the word "why", which is idiomatically used in rhetorical questions to express anger – can be construed as an insult. If you ask "why do you think he is crying?" in the right (or rather wrong) tone of voice and context, it will be construed as your having said, "What's kind of idiot are you that you mistakenly think that he is crying?"
As someone who has to ask both the "what are your reasons for thinking this" and the "what do you think his reasons are" questions on a regular basis, and make sure that I keep them distinct and don't antagonize anyone I ask them of, I'll tell you: there is no simple easy grammatical way to do so.
The way I do it is by explaining myself in detail using lots of words, and/or by pursuing the question by entirely other words:
How did you know he was crying?
What did you see that let you know he was crying?
Did you see him crying?
What reason did he have for crying?
Did he say why he was crying?
I wonder why he was crying.