Hi,
Does this phrase "if only because" mean "at least for one reason" or "only because of that reason" ?
You have the right idea.
Consider these examples.
Tom loves Mary, only because she is rich. That's the only reason he loves her.
Tom loves Mary, if only because she is rich. There could be other reasons involved. But that's the only reason we are sure about. The implication is that he should love her for better reasons.
Best wishes, Clive