A person can cry for multiple reasons.
I believe that Jesus wept because of a deep compassion for their grief. Not the professional mourners... but those who loved Lazarus.
I go to funerals for the living, not for the dead. If one of my friend's has a loved one who dies, I go for that friend and lots of times, I cry because they are grieving. When we know the person who died is a Christian because of his fruit, we know he is in a better place. (I am usually very jealous that person is in heaven--at least for a few minutes anyway.)
However, our hearts have an Eternity factor in them because of the eternal Holy Spirit. When a person dies, that breaks the eternal fellowship for a time and the grief caused by the breaking of fellowship is because of this hiccup in the eternal flow.
Yes Jesus knew what He was about to do. He'd planned it four days before. Yet, it still does not stop His compassion from being exercised for those whom He loved.
In Luke 16:31, Abraham tells the rich man, "...they have Moses and the prophets, if they do not believe them, they will never believe even if one rises from the dead." Jesus wept because he knew they would never believe.
Another time He wept is when He mourned over Jerusalem.
Matt 23:37 O Jerusalem, Jerusalem, putting to death the prophets, and stoning those who are sent to her! Again and again would I have taken your children to myself as a bird takes her young ones under her wings, and you would not! How His grief poured over Jerusalem when He said, "See your house is laid waste."
The grief of rejection. To have so much to give and to know that if only the gift is accepted that the loved one would not suffer the Wrath of God... that could make any ordinary person go crazy. I can remember having a screaming mimi fit at my children when they did stupid, idiotic things. But...