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Tearjerker: Pacific Rim
The whole fact that Raleigh was linked to Yancy as he was killed by the Kaiju, making the experience all the more traumatic though experiencing all of his pain and despair in that moment.
Yancy: Raleigh listen to me. Raleigh listen to — (ripped out of the Conn-pod by Knifehead)
Worse is when Raleigh forces himself to pilot his Jaegar to shore and stumbles out of the cockpit. He just walks around dazedly, repeating Yancy's name before collapsing.
Look at it from the perspective of the old man and his grandson who saved Raleigh. They just watched a Jaeger, the pinnacle of human engineering, a walking god-like warrior just stumble and fall to pieces before them, and out of the Jaeger walks a single wounded, delirious pilot, when everyone knows that pilots are paired. When the old man falls to his knees beside Raleigh, you can see how horrified and crushed he is just by the implications of Gypsy Danger falling dead in front of him. The Jaegers aren't invincible.
The demise of Cherno. While both Typhoon and Striker's pilots were killed quickly, the Kaidonovskys got to enjoy a Rasputinian death until the kaiju found the cockpit. The Hope Spot didn't help.
Herc and Chuck Hansen's goodbyes to each other.
Herc: Stacker, that's my son you've got there. My son.
The worst part is how it all plays out. Pentecost and Chuck know they are going to die, and they've already accepted it.
Really, Herc's lot in life in general. He loses his wife, his young son, his closest friend, numerous family members, and several of his fellow pilots and is left with nothing but his dog, Max.
The fact that Chuck took the time to say goodbye to Max, and that he's going to miss him.
Chuck: Hey, handsome. Oh, I'm gonna miss you. You look after him for me.
Mako's flashback, revealing a scared little girl bawling her eyes out after losing her parents in the middle of a devastated Tokyo.
Perhaps even worse on Stacker's end. He's essentially taking his closest friend's son to an inevitable death. Considering how close and long Stacker and Herc have worked together, it's very likely that Stacker has known Chuck since he was a little boy, or at least a young teenager. Just imagine taking someone who you've mentored since they still had baby teeth into such a terrible situation.
Mako's final words to Pentecost are "I love you". Doubles as a super-sad Bilingual Bonus since she says it in Japanese with no subtitles. This was intentionally left untranslated, because her words were only for him.
Very briefly, among the scattering of images/memories that show up when Gottlieb and Newton drift together interspersed with the shots of the Kaiju is... a young boy crying and hugging his knees. Judging from the clothes and setting, it's a very young Gottlieb. What happened to him?
The novelization states he was bullied as a result of being a Child Prodigy.
The fear Mako shows when she thinks that Raleigh died.
This deserves further mention. Think of who Mako has already lost at that point: her entire family when she was a child, several Jaeger pilots (Chuck, the Wei triplets, etc.) who she has likely known for many years, and, mere moments earlier, her adopted father. Now imagine her thinking she lost someone who she shared a strong mental connection with. It's not hard to imagine her thinking she's cursed to lose everyone close in her life at that moment.
The novelization, and likely cut scenes, show why Chuck has a chip on his shoulder towards his father. Hercules could only guess as to where his wife and son were with only an hour before the fourth Kaiju, Scissure, would be nuked. Herc picked his son to save and would never know if his wife died by the Kaiju or nuke. Every time father and son drift Herc knows his son begrudges him but they still love each other. Despite any decent parent preferring their child be saved instead of them, Chuck still has unresolved anger. Drifting somehow makes it better and worse.
And then, in spite of everything, Chuck ends up being killed by a Kaiju, anyways.
One of the deleted scenes included on the DVD had him calling out that Herc never raised Chuck to be anything, and that the only reason they're still together after all this time is because they're Drift-compatible, so they don't even need to talk to each other outside the Conn Pod. The look on Herc's face is heartbreaking.
Chuck: After Mum died, I spent more time with these machines than I ever did with you.
Honestly, Chuck's whole life in general. He's been raised since early childhood to be the perfect Jaeger pilot, has an extremely strained relationship with his father, displays many of the unhealthy habits and emotional issues that are commonly attributed to Child Soldiers, and willingly sacrifices himself without a second thought to his own future. In the books, Chuck's greatest wish was to be able to live his own life and make decisions for himself, instead of always having the fate of humanity pressing down on him. He never gets to experience this.
"Well, my father always said, he said if you have the shot, you take it. So let's do this."
This was the first and only time Chuck referred to Herc as his father, not the derisive "Old Man/Dad". Herc's reaction as he closes his eyes, his expression a mix of pride and grief, makes this scene all the more heartbreaking.
When Pentecost reveals he'll be Chuck's copilot, he and Mako have a quick heart to heart about her protecting him. The look on her face is heartbreaking, since she already lost one father, and she's about to lose another.