Perhaps Jesus wept because His Divinity wanted to share with Humanity’s tradition and emotion of grieving for the dead. Just as His Divinity joined in suffering with His Humanity for our redemption at Calvary, so His Divinity also joins with His Humanity in other human emotions and life events, grieving for the dead being one example.
This is also seen when Jesus is baptised by John the Bapist. Jesus’s baptism was not necessary for His sanctification, as he was holy from the moment of his conception. Jesus’s Divinity chose to join with His humanity in the event of Baptism so as to make more complete and harmonious the life of God with the life of Man, and, of course, to set a good example.
Another example might be Jesus’s joining in the celebration of the wedding at Cana. His Divinity chose to participate in this event to further unify events in the ordinary life of man with the extraordinary events in the life of God. He makes the ordinary extraordinary. As man rejoices at such an event, so God also rejoices, the lives of man and God reflecting one another in greater harmony.
Jesus Humanity made holy all the ordinary occurrences and traditions in the lives of men by having his Divinity operating in those actions.
So if we, when we are weeping for the dead, join with Jesus’s weeping over the death of Lazarus, we can make our act a form of reparative suffering and or prayer. If we, when we are rejoicing over someone’s matrimonial union, join our celebration with that of Christ at Cana, our rejoicing can be like a form of prayer. Etc, etc …
This is my opinion on the matter, of course.
Hope this makes sense.
God bless!