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Tear Jerker: VeggieTales
The silly song "Pizza Angel" is one of the saddest things in the show. It even ends with Larry, one of the funniest characters on the show crying because his the delivery guy ate his pizza.
Larry: "Pizza Angel, I'm on my knees. You'll live forever in my memories.''
In "It's a Meaningful Life", which has an obvious It's a Wonderful Plot, the character Stuart see what would happen if he left his hometown to become a big football star. What he sees that in this alternate reality his hometown is terrible but the worst part for him was seeing his adopted daughter alone in an orphanage, unloved.
During the "Easter Future" segment, Ebeneezer Nezzer is seeing the horrors of what would happen in a world without the "hope of Easter." But the thing that pushes him over the edge is seeing Edmund's gravestone. Arguably, making this one of the most convincing changes of heart for a Scrooge type character ever portrayed in media.
Ebeneezer's entire motivation is that he just can't move on from the death of his grandmother and is just not okay with the idea of death in general. There's a moment during "Easter Present" when he becomes very upset when he learns Edmund could very well die from his illness and his parents already know. Even Hope, who up to that point had been rather harsh with Nezzer, tries to put out a hand to comfort him in this scene.
There's a scene where Reverend Gilbert tries to console Edmund when Edmund worries about Nezzer's intentions to tear down St. Bart's Church. Not only is it very sad to see a small child worrying about something like that, the scene becomes sadder when you realize that Reverend Gilbert is himself worrying about the fact that Edmund's illness is slowly killing him. The look Edmund's parents exchange with each other after Reverend Gilbert leaves Edmund's room...
King George and the Ducky: Being sent to the Pie War causes Thomas to go insane. It's heavily Bowdlerized from the Biblical story it's loosely based on (Uriah actually died), and Thomas does get help at the end, but it still wasn't pretty.
In The Penniless Princess, which is based on A Little Princess, they did not soften the scene where Sara learns her father has died.
Even worse? Her father was played by Larry.
The End of Silliness. Larry's nightmare at the beginning, and then seeing him absolutely miserable through most of the rest of it. It's so unlike his usual cheeriness, and really makes you feel sorry for him.