We are told that he cried because he saw with nevuah that she was not destined to be buried with him, and she would die young. As to the rest – I have always wondered about that since we learn out that the Avos kept TARYAG mitzvos, and Yaakov Avinu in particular stated, “Im Lavan garti, v’es TARYAG Mitzvos shamarti.”
I have never heard a really good answer to this question. Even the “it was not derech chiba” doesn’t really answer the question, ebcause there are many issurei nigiah that are clearly not derech chiba for those who are not shomer. Shaking hands is a very good example. Still assur.