For whom do those tears fall?

One of the most heart-wrenching moments in The Lord of the Rings comes at the end. Frodo has left the Shire and is about to sail across the sea to the Grey Havens, and Sam, Merry and Pippin are there to witness his departure.

“You tried to give us the slip once before and failed, Frodo,’ he said. ‘This time you have nearly succeeded, but you have failed again. It was not Sam, thought, that gave you away this time, but Gandalf himself!”
‘Yes,’ said Gandalf; ‘for it will be better to ride back three together than one alone. Well, here at last, dear friends, on the shores of the Sea comes the end of our fellowship in Middle-Earth. Go in peace! I will not say: do not weep; for not all tears are an evil.'” 

What Gandalf says is true; not all tears are an evil. But many of them are selfish. An example: someone I love passes. Naturally, I cry. But for whom do those tears fall? Do I weep because the world has lost such a person? Do I despair because that individual will never feel the wind, see the sky or know a smile? Or do the tears roll down my cheeks because I won’t experience their company again? Do I mourn the dead, or the living?

These are hard questions, but they must be asked. Is my grief true, or is my grief a selfish sorrow?