This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / The Kingkiller Chronicle
The whole sequence where Kvothe loses his parents and his extended family.
In the framing story, when Kvothe goes out to the woods and cries over the awful memory of his family's death.
Kvothe's cruel stay in Tarbean
Kvothe: I found some empty crates in an alley. I curled up behind them, bruised and weary. I closed my eyes and tried not to remember what it was like to go to sleep warm and full, surrounded by people who loved you. That was the first night of nearly three years I spent in Tarbean.
Particularly his father's lute being broken on the first day.
And Trapis, who's basically a heartbreaking moment on two legs. He spends all of his time on his bare feet in a cold, stone cellar taking care of hundreds of homeless children - lonely, starving, defenseless, broken, hated children - giving them everything he has, which is so little it cannot be measured. Nothing he does can ever make a noticeable difference in the larger picture of the city, and the most he can ever hope for is to see the back of maybe one kid in a hundred who makes it out. Kind of makes you think there's good people in the world.
There's small moment of heartwarming when Kvothe describes how these homeless children feel about Trapis.
Kvothe: In return we loved him with a silent ferocity that only animals can match. If anyone had ever raised a hand to Trapis, a hundred howling children would have torn them to bloody scraps in the middle of the street.
And taking a life-threatening beating,then almost dying alone in the snow on the equivalent of Christmas. And the only person to stop and help him is dressed as the worst of demons, and supposed to be out causing the worst of mischief, and he does it while a woman tries to drag him away to have fun.
The reason why he was beaten almost to death: He was begging for the first time in a wealthy part of town and a woman who takes pity on him gives him a large amount of money. Immediately, a city guard sees what happens and chases Kvothe down. Not to take the money back, not to discourage begging; the guard gives Kvothe a vicious beating, broken ribs, and leaves him to die from hypothermia just to teach him a lesson: you're not welcome here.
Kvothe crying about missing his mother in Auri's arms while he's under the influence of the plum bob.
Auri's presents to Kvothe: a candle she made herself, a kiss on his head, and a bed for him in the Underthing in case he needs a safe place to stay. It goes to show just how much Auri cares for Kvothe. The Slow Regard of Silent Things makes this even more Heartwarming in Hindsight. It shows just how hard Auri worked to make those things, and how much she struggled to come up with the idea.
Kvothe's argument with Denna after he first heard the Song of Seven Sorrows. So true.
After his argument with Denna, Kvothe is determined to write her a letter explaining the truth behind why he said what he said -about the death of his family and his encounter with the Chandrian.
Kvothe: Hours later the blank sheet still stared at me, and I beat my fist against the desk in fury and frustration, striking it so hard my hand bled. That is how heavy a secret can become. It can make blood flow easier than ink.
The whole sequence after Kvothe kills the fake troupers is god awful. We get to see that one of the girls who has been raped four times a night repeatedly has caused her to be driven the next best thing to catatonic. Not to mention Kvothe's own reaction to them killing and impersonating a troupe is heartbreaking, you can just feel the sadness underneath the anger:
Kvothe: "You thought you could fool me?" I said, feeling my anger coiling inside me like a spring. "This is my family! How could I not know?"
After Kvothe follows Denna without her knowledge, he learns some interesting things about her. He describes it by mentioning the philosopher Teccam, who had this to say:
Kvothe: Secrets of the heart are different. They are private and painful, and we want nothing more than to hide them away from the world. They do not swell and press against the mouth. They live in the heart, and the longer they are kept, the heavier they become.
Teccam claims it is better to have a mouthful of poison than a secret of the heart. Any fool will spit out poison, he says, but we hoard these painful treasures. We swallow hard against them every day, forcing them deep inside us. There they sit, growing heavier, festering. Given enough time, they cannot help but crush the heart that holds them.
Modern philosophers scorn Teccam, but they are vultures picking at the bones of a giant. Quibble all you like, Teccam understood the shape of the world.
After making it back to Severen, Kvothe goes to look for Denna and finds a note waiting from her... except that the illiterate innkeeper didn't realize that it was the note Kvothe had sent to her, still unopened and unread, having arrived too late.