I wonder if He wept in empathetic compassion at the sadness of those He loved.
I think this is very true. There is something else I see here. Jesus waits for his friend to be dead. Properly dead. He knows this is a demonstration of Jesus's authority over life and death, so that his death is understood as a true sacrifice, a giving up of his rights, not a defeat.
So he visits his friends. They are all truly grieving at the death of their friend. But still they do not see that Jesus is God made man. The pharisees are cynically watching over the events to see what the "fake" prophet will do. Everyone is sure he is a healer, but raising anyone from the dead, nope.
After all his efforts, his patience, still he knows here is a defeated, bowed people, with little focus on reality and freedom in the power of God. All these ingredients would be there in a weeks time, but he would be the one in the tomb, and it would be the Father who called Him out. Now that is truly an emotional overload. Look forward a week to Gethsemane and still the true burden is very hard to bare. In another sense also this place is very, very alone, even in the midst of friends.