The verse in Greek actually reads "i?sous o edakrusen" and literally translates into "the christ shed tears" or as "the anointed shed tears." Translators shortened "shed tears" to "wept" because the former conveys a sense of "silent mourning" while the latter conveys "loud emotional wailing". They thought that portraying God as "silently crying" gave off an air of emotional detachment. Whereas "weeping" lends to more "dramatic show".
It's the shortest verse because, well, umm, it contains only 4 words in literally Greek linguistics; 3 words in English "dynamic equivalent" translation; and 2 words in shorten English "DE" translation. The original Greek manuscripts don't contain chapter and verse distinctions nor capitalization of "Lord," "God," "Jesus," or "Lazarus". These are all English translating embellishments to make the text keenly readable.
Commentators tend to "play up" this scene as though Jesus was showing the quintessence of human emotions. "Crying over the loss of human life." While this is all fine and dandy, you cannot find other verses of Jesus "crying over dead humans". The explanation commentators give seems a bit scripted to such and such doctrine. And no, Jesus doesn't say anything immediately afterward. Others do.
A likelihood of why Jesus "cried" could be that Jesus and Lazarus were GOOD friends. Verse 36 says, "Behold how He loved him." The Scriptures specifically tell us Christ loved Lazarus (not a homosexual love as some like to play around on). But this is "brotherly love". The Scriptures are probably silent on their close friendship as to not later lead men into conjecturing false interpretations and far-fetched presumptions.
So Jesus wept over Lazarus because He lost a good friend.