So, in short, what are the difference in usage between these words? Both seem to mean reason.
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原因 is cause, whereas 理由 is reason. They are similar, but the former assumes there was an observable but unexpected "event".
When you are describing the reason for something that is always true, you should use 理由:
In the following example, 原因 sounds like the speaker is asking about the direct cause (e.g., traffic accident), whereas 理由 may sound like the speaker is asking about more indirect or ultimate reasons (e.g., fate, grudge).
According to jisho 理由 means "reason, motive" and 原因 means "cause, origin". Thinking in terms of their translation 理由 would have something to do with your goals (what do you want to get?, for what did you do it?) whereas 原因 would be closer to "initial reason, cause" (what caused the accident? what happened and made you do smth?)
Note that I only think in terms of english here but some examples seem to correlate with my reasoning:
別の理由があるね？ (there is another reason isn't there?)
事故は彼の不注意が原因だった。(the accident was due to his carelessness.)