This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Muppet Christmas Carol
The song "When Love Is Gone," which was removed from most versions of the film, is quite sad.
Present Scrooge joins in and practically breaks down when he realizes that Belle is and was totally right.
Same goes for Rizzo, who is sobbing his eyes out as Gonzo tries to console him.
Before the song starts, there's the conversation between the young Scrooge and Belle. He insists he's putting off their wedding because he loves her. Belle calmly (but no less heart breaking) replies "You did once".
Then there's Scrooge's pleading at the beginning of the scene, "Oh, please, spirit, do not show me that Christmas."
At the end, after Scrooge tells the spirit to leave him, there's a quietly heartbreaking instrumental reprise of the song as Scrooge finds himself back in his bedroom and sits crying on his bed.
When "The Love We Found" kicks in at the end it becomes heartwarming and sad at the same time.
Rowlf is reduced to a cameo as the pianist at the Fozziwig Christmas party, despite being a major supporting character in earlier films and shows. This is because of Jim Henson's death and the Muppet crew at the time felt that they didn't have a performer who could do that character justice. He wouldn't start to speak again until the late 1990's, when Bill Barretta took over the role.
Tiny Tim's death has Scrooge initially relieved at being at the Cratchit house again, until he realizes how quiet it is.
When we see the Cratchits during Christmas Present, Piggy is hunched over the stove, stealing chestnuts. During Christmas Yet To Come, she's in the exact same position, until you realize that she's bent over the stove crying. This is made worse by Scrooge's reaction with his voice breaking as he pleads "not Tiny Tim".
"I think (Dad)'s walked a little slower these past two evenings." That line just sets the tragedy up so mercilessly. The entire scene is near impossible not to weep at.
When Bob says he arranged for Tiny Tim to be buried on his favorite hilltop, he tries describing it to Emily. "It would do you good to see how green the place is. It's...it's near the ducks on the river. Tiny Tim..." He's too broken to finish, so Emily quietly responds, "Tiny Tim loved watching the ducks on the river."
When Kermit/Bob's voice breaks on his son's name as he says, "Life is made up of meetings and partings; that is the way of it. I am sure we shall never forget Tiny Tim, or this first parting that there was among us." This is followed by a slow pan to Tim's empty chair and ownerless crutch, to the swell of a French horn wistfully reprising "Bless Us All"...
Kermit's speech is especially poignant when you remember this was the first feature film after Jim Henson's death, as well as the first to not feature Muppeteer Richard Hunt, who succumbed to AIDS shortly before production began. (Many of Richard's characters were since Demoted to Extra.) And the whole scene became that much more moving after Jerry Nelson (Robin/Tiny Tim) died in 2012 after suffering from emphysema for over a decade. The disease caused him to have an Incurable Cough of Death not unlike Tiny Tim's in the film. Not only that, Jerry had a daughter (Christine) who died of cystic fibrosis...a symptom of which is a cough.
Seriously, if you're not sad enough from Kermit's speech as it is, you can replace any time he says "Tiny Tim" with "Jim Henson" or "Richard Hunt" and the tears will be flowing in seconds.
Most of the beginning of the scene echoes the Christmas Present scene—Piggy at the stove, Peter turning the spit, the girls talking to Piggy, but their reactions are so subdued that you know immediately what happened. For example, when Kermit enters, the kids go to greet him- but while they cheered and practically ran him over in the Christmas Present version, they just say "Daddy" and give him a quiet hug. And as mentioned above, instead of cheerfully bustling around and stealing chestnuts, Piggy is crying.
Tim's illness, first when he gets excited about the dinner and then at the end of "Bless Us All," when he coughs after singing the last note. The song is cheery but that cough is a reminder that the family, while together now, may not be complete in the future and they move on to the dinner to keep up their spirits. You can see Scrooge looking moved, before he asks the Ghost of Christmas Present if Tiny Tim will live.
After he first sees Tiny Tim with Bob, Scrooge can only say "a remarkable child". You can see him realizing that this is what Bob comes home to.
Scrooge suffers a massive Heel Realization during this scene, lamenting that he pays Bob so little and also clearly sorry for how small the Christmas dinner is as a result.
The dedication to Jim Henson and Richard Hunt also invokes this on a meta level.
Scrooge's reaction to hearing that he was the subject of Fred's mocking round of Yes And No is heartbreaking. When he realizes the group is laughing about him he just looks completely broken and sad. It's a testament to Caine's skills that he manages to convey it so powerfully in just a few seconds.
The revelation in the Christmas Yet To Come that Scrooge is going to die unloved and alone. The slowness of the scene and Scrooge's reactions suggest that he realized the identity of the reviled dead man early on, and has been in denial about it.
And in this scene, Scrooge's tears are clearly him realizing that he is the reason for Tiny Tim's death.
The Ghost of Christmas Present's death, ageing and turns to glittering dust after Scrooge has just befriended him and begs him not to leave him.
The regret in Scrooge's face and voice when he sees his boyhood self all alone in school at Christmas. It gets worse when he remarks that it'd be pointless for Christmas Past to show him another of his childhood Christmases. They were all the same and he was always lonely.
In the same scene, there's something horribly sad of Scrooge watching his childhood pass before him in a flash, realizing just how quickly his youth disappeared and how little he was able to enjoy it.
"One More Sleep 'Til Christmas" is very heartwarming; everybody's so excited and happy because it's Christmas time, Kermit smiles at the stars and heads home... and then the shot scrolls on a few sad notes to a shivering little Bean Bunny, curled up in newspapers and trying to keep warm, all alone on Christmas Eve.
The overall melancholic feeling that runs through the majority of the story anyway is present here, even though they try to keep things as light as they can. Since this was also the first Muppet movie produced without Jim Henson, there is a lot of sadness running through the film.
It's relatively small compared to a lot of the others but Michael Caine's reaction shots during "Bless Us All" are enough to make people tear up. You can practically see the exact moment in the song that he realises what a jerk he's been to Bob (and, by extension, Bob's family) as well as the moment he realises his own culpability in Tiny Tim's poor health. There's also the Fridge Horror (Fridge Sadness?) of the fact that we already know Scrooge suffered a cripplingly lonely childhood, meaning that this is potentially the first time he's truly seeing a happy family enjoying Christmas even though they have practically nothing to celebrate it with. The sight of him clearly silently fighting back tears is almost more heartbreaking than seeing him openly crying.