This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Capitol Critters
The pilot episode. Poor, poor Max loses his entire family to exterminators and is forced to pack up and leave for DC at a moment's notice. The scene at the end where he cries to Jamett on the helicopter is pretty heavy as well.
Felix's death in A Rat To Bear Arms.
In the episode A Little Romance, Max saves a girl mouse from a cat by knocking the cat out with a stage light. He thinks he killed a cat and when congratulated by the girl's parents, he breaks down in Tears of Remorse, explaining that he didn't want to kill the cat. Considering the fact that he watched his own family get gassed to death in the first episode, he becomes an even bigger Woobie in this one. Then there's the end of the episode where Max bids Miko a tearful goodbye and Trixie tells Max that the only reason he wants to go to Japan with Miko is so he can feel like he's part of a family again. Max then goes on to describe that some nights, he misses his parents so much he can't go to sleep.
The episode "Opie's Choice" is a strong example of the kind of mature, boundary-pushing series it wanted to be. For one thing, Max is nearly murdered by drug dealers who force pills down his throat, sending him into a coma. To say nothing of when we see how badly and realistically Opie's drug addiction has affected his family.
Muggle's Disney Death in The Lady Doth Protest Munch and Max's tearful reaction to it. Heck, pretty much anytime Max cries.
The end of If Loving You Is Wrong, which shoves Jammet straight into Jerkass Woobie territory.