Depends why they are crying, how often they cry, where they are doing it, etc. I don't really think I can classify it as a strength or a weakness. It's just a reaction after all, though it can be an gauge for how hurt the person is.
Kinda like, if there was a scale from 1 - 10 and, once you reach a certain number, you start crying. Just because someone cries at 2 doesn't make them weak, it just means they are affected by things more. However, you never know if the pain they are going through is a 2 or a 10 because they cry so often people don't understand if it's just slightly bugging them or something that totally destroyed them.
On the other hand, if a person never cries and then you see them cry, it can show how deeply they are impacted. It's kinda like swearing in a sense. If someone never swears, it's a big shock when one flies out of their mouth and you realize that they really are upset.
To me, it's never really a weakness, but sometimes people abuse the implied meaning behind it. Most people cry cause of pain or frustration. Sometimes it's cause you're truly touched by something, but let's ignore that for a moment. With the other two, others feel bad and want to make the person better and this is where it's abused to get attention.
I knew a girl who told me she cried so her boyfriend would do things for her. One of my guy friends told me about a guy who would cry so girls would sleep with him. Then there are the people that cry over everything. If you want to do it, fine, but don't be surprised it others get annoyed with it or assume you're doing it for sympathy.