I am going to assume this question refers to crying in front of someone rather than crying period. In that case, it is a weakness. I am an old fashioned man about this. It does not matter if you are crying over a woman, a baseball to the groin, or a moving rendition of "America the Beautiful," your emotions got the better of you. It lets people know how to get to you. When thery learn how to do that, you have lost something valuable.
That is not to say men cannot cry. I have had some humdinger Tammy Faye moments myself. but I think those ought to be private moments. The stoic in me has made a Herculean effort to keep them that way. I have failed a few times, which confirms my belief about public cryying as far as I am concerned.
Yes, I know Jesus wept openly before Lazarus' tomb. The shortest verse in the Bible notes the occasion specifically. One has to assume that means it was a significant event. Perhaps to show jesus' human frailties? Wiser theologians can weigh in on the matter in the comments, but I am sticking to my answer of public crying as proof of weakness.