This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Almost Human
Episode 2 - Skin
Victor (a child), being taken to the police station, he had to be cared for because his mother was kidnapped. After being questioned he asked John 'when will his mommy be back.'
Dorian becoming squeamish during an autopsy on a mutilated sexbot.
Vanessa, Sex Bot, being deactivated because her existence was illegal; she was created with combination of android parts, human skin, and DNA.
Episode 5 - Blood Brothers
Maya got the Cerebellux implant so she could psychically reconnect to her parents after they died. But before she could get back to her house to get items to touch to initiate the reconnection, her house burned down.
Episode 6 - Arrhythmia
The decommissioned DRN is a sad look at what Dorian's fate could easily have been had he not been assigned to Kennex. That Dorian lets him keep the memory of his proudest moment and closest human connection takes a bit of the sting off, but it's still a little heartbreaking that, after giving him back his case files and letting him feel like a cop again for a short while, in the end it has to be taken away again.
Episode 7 - Simon Says
The first collared victim, Ramon, couldn't be saved. His last request was for the detectives to tell his wife that he loved her.
Rudy rambling to Dorian that one having their own place isn't all that it's cracked up to be, it can be lonely.
It all turns out okay in the end though - guess who Rudy's new housemate is!
Episode 8 - You Are Here
Anton, a software engineer, is forced into creating an assassin bullet. He is presumed guilty until it is later revealed that he sold the technology to protect his girlfriend and her daughter. The girlfriend, Kira, is brought to tears knowing he died protecting them.
Episode 9 - Unbound
Even meeting Dorian wasn't enough to stop Nigel from continuing with his plans.
John: Must be a hell of a thing to meet your maker. But to be betrayed by him...
Episode 10 - Perception
A mother, Mrs. Hoving, stresses about her daughter, Lila, having to compete with genetically enhanced children called 'Chromes'. Due to the pressure she places on her daughter (who took drugs in an attempt to enhance herself), she inadvertently is the cause of Lila's suicide. Even with knowing the truth she still holds disdain for Chromes.
Episode 12 - Beholder
After all the horrible things that Eric Latham has done to make himself look "perfect" for his beloved Judy, he finally meets her... and finds out that she's blind. She never cared what he looked like.