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Tear Jerker: Primeval
The conclusion of the fourth episode, when Connor comforts his delirious best friend as he slowly dies from the parasite. And afterward, he stands up and turns to Nick and says that he can't handle being part of the team anymore, and Nick gives him a hug.
When Abby is (apparently) lost forever to the Mer creatures in 2.4. Seeing Connor so distraught and nearly in tears is especially heartbreaking considering the bad feeling the two of them had been sharing directly prior to it. Worse still, Lester (who is still a Smug Snake) orders him to go home and do nothing.
Shortly thereafter, Cutter's death during season 3, particularly his last words. This soon prompted the real heartbreak of Jenny leaving the Arc, closing the chapter for good on Cutter and Claudia/Jenny.
The characters' reactions to seeing him dead make half the Tear Jerker, particularly Lester shouting angrily for an ambulance, in frantic denial.
The death of the high school girl at the jaws of the Therocephalian in 4.4 is rather devastating, especially since they play it up to make you think she might make it.
Jess's reaction, too.
Nick tearing up the photo of Claudia, showing he's finally given up on getting her back.
Jenny finding it again after his death, taped back together. Guess he really couldn't let go after all.