What the Bhagavad Gita says about grief
The Gita begins and ends on the same word. Arjuna collapses in grief at the end of chapter 1, and the last thing Krishna teaches him, in 18.66, finishes with mā śucaḥ: do not grieve. Everything in between sits inside that frame.
What the book does not do is argue that the grief is unreasonable. Krishna's opening move in 2.11 is sharp, telling Arjuna he grieves for those who need no grief while speaking words of wisdom, but the sharpness is aimed at the reasoning rather than the pain. The arguments that follow are about what is actually lost when a body ends.
The gentlest verse on the subject is 18.54, which describes somebody who neither grieves nor wants, the same towards everything alive, and then says that person comes to the highest love. The steadiness is not the destination. It is what clears the ground, and what it clears it for is warmer than itself.
The verses 13
1.47
Sanjaya said: Having spoken so, Arjuna sank down on the seat of the chariot in the middle of the battle, letting go of his bow and arrows, his mind overwhelmed with grief.
2.1
Sanjaya said: To him, overcome with pity, his eyes full of tears and clouded with distress, sunk in grief, Krishna spoke these words.
2.8
I cannot see anything that would drive off this grief that is drying up my senses - not an unrivalled and prosperous kingdom on earth, not even lordship over the gods.
2.11
Krishna said: You grieve for those who need no grieving, and you talk like a wise man while you do it.
2.25
It is called unshowable, unthinkable, unchangeable.
2.26
And even if you think it is constantly born and constantly dies - even then, strong-armed one, you have no reason to grieve.
2.27
Whatever is born will certainly die, and whatever dies will certainly be born.
2.28
Beings are unseen before they begin, seen in the middle, and unseen again at the end.
2.30
The one who lives in the body - in everyone's body - can never be killed.
5.20
He does not leap up when something pleasant comes, and does not recoil when something unpleasant does.
12.17
Who does not rejoice and does not hate, does not grieve and does not crave, who has given up both the lovely and the unlovely, and is full of devotion - that one is dear to me.
18.54
Having become the absolute, clear in himself, he does not grieve and does not want.
18.66
Let go of all duties and come to me alone for shelter.