This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Over the Hedge
In the TV scene, RJ changes the channel a lot, but keeps switching to things talking about betrayal (E.G."We let you into this family, and this is how you thank us?"), culminating in him switching to a Dr. Phil-like show where he mouths the words "I am a dirtbag."
Hammy's quiet and heartbroken "I'm not stupid...". It takes on a new meaning moments later when he quietly repeats it in an angrier tone, making it sound as if he's saying "I know exactly what you think of me" and letting it be know that he's lost all respect for his friend.
"Still" may be one of the saddest songs Ben Folds has ever written.
RJ taking the Spuddies and leaving the kitchen. This is after he accidentally revealed his plan to the Verne and the others. The sad looks RJ and Verne give each other before RJ leaves the kitchen along with music is heart-breaking.
The scene where the animals are all in crates after RJ takes the food and leaves. Their reaction is really what sells it.
Heather: I don't want to die, Dad. Not for real.
Ozzy: There there, sweetheart... we'll be okay.
It's a little Fridge Horror thrown in when you start wondering what happened to Heather's mother.
Shortly after, there's a completely dialogue-free moment of Stella reaching through the bars of her cage to hold a trembling Hammy's hand.
A blink-and-you-miss-it moment: When the caged animals are being loaded into the van, right before the scene cuts back to RJ and Vincent, Hammy can be seen putting his paws to his face, possibly implying that he's actually crying.
When Ozzie thinks Heather is dead after she gets kicked by Gladys. Besides the fact that the poor guy thinks he just witnessed his only child get killed in a pretty brutal fashion (a less than ten pound possum getting kicked several feet into a wall is pretty brutal, even without any signs of trauma), which is sad enough, it becomes worse when you realize that Ozzie no doubt felt like he had lost everything, since his wife appears to have died before the start of the film, and now he thinks his daughter was killed as well.
It doesn't help that you get a quick glimpse, right before Heather 'wakes up', of Ozzie silently sobbing.