This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / In the Heights
Especially Usnavi's speech at the start of the song. "They said a combination of the stress and the heat, why she never took her medicine, I'll never understand. I like to think she went out in peace, with pieces of bread crumbs in her hand."
"When she was here, the path was clear/And she was just here/...She was just here..." Sob.
And the song that follows — "Everything I Know".
"Inutil". It's a bit harder to understand if your one or both of your parents isn't like Kevin...from a different country...working their ass off...just so their kid can have a good future....'scuse me.
Heck, from a different country nothin'. This troper was near in tears because her father (American born and raised) pretty much exists based on the one line "I will not be the reason that my family can't succeed."
When this troper saw the show, the actor's voice broke on "and he slapped my face." Not sure if it was intentional or not, but it was totally heartbreaking.
Believe it or not, the end of "Carnaval de Barrio". It's a very happy, celebratory song...but it ends with the Piraguero and Daniela singing "Esa bonita bandera! Contiene mi alma entera!" ("This beautiful flag, it holds the whole of my soul"). It may not seem like much, but in a country that's currently having a lot of problems with immigration and racism, a stage full of characters taking pride in their heritage moves this child-of-immigrants troper to tears.
Plus Sonny's solo in the song shows that he's terrified of his neighborhood disappearing, despite his status as Plucky Comic Relief and sees everyone party and celebrating as them ignoring what's going on around them.
And "Paciencia y Fe"
Pretty much the entirety of "Finale", especially:
"Tell everyone we know. Sonny..." Sonny hugs him and Usnavi softens and hugs him back. "Alright, go."
"Abuela, that ain't a stoop, it's your throne."
"I found my island, I been on it this whole time."