Bitey of Brackenwood is a complete ass, going out of his way to ruin the day for Brackenwood's other creatures. It is eventually revealed that he acts out of jealousy. He can't stand seeing other creatures happy with their kin, and being the last of his kind compounds this jealousy.
Tom of Echo Chamber. While Tom is an ass to everyone and his excuse for being so is...weak, when he actually admits why he struggles, he shows a scared side. Especially obvious in "Romantic False Lead", when Tom's reasons for loving Porn Girl is that she doesn't threaten, scare, or hurt him.
Both Zaboo and Bladezz from The Guild. The first is a Stalker with a Crush who's just so naive and well-meaning that Codex can't figure out whether she wants to ignominiously boot him out of her life or hug him. The second is a troll and a bit of a Jerkass, but he spends much of season 3 having incredibly nasty stuff happen to him.
Also, Tink, although she's more Jerkass than Woobie.
Zaboo is creepy and horrible with people, yeah, but he doesn't qualify as a jerkass. Even when he does rude things, it's always done with the best intentions and a loving heart. He's just...super creepy. (And a complete Woobie.)
Efeddre of Guts and Sass: An Anti-Epic has a Dark and Troubled Past where he was captured and tortured for nine years. He regularly verbally abuses the people who rescued him, but few feel like they can smack him because it's only been a year since he was rescued.
The Green Goblin from I'm a Marvel... and I'm a DC. The poor guy is always getting beaten up (even though this is Played for Laughs) and the object of his affection is hopelessly devoted to her abusive boyfriend (the Joker). Of course, he does treat his son like garbage.
Jackie from the Jerry series. In the original short, she steals from the protagonist twice. In her own short, she cheats on her boyfriend, beats the shit out of several people, and maces a guy for giving her a flower because he was ugly. And, she gets kicked out of their house, has her suitcase stolen, gets sexually assaulted, gets mugged, becomes a stripper, breaks her ankle, gets sexually assaulted by her doctor, does heroin, etc. The whole thing karmically balances pretty well.
The critic himself pointed this out in his editorial "Why is Loki so Hot?", in which he looks up this article to prove a point about Loki of the The Avengers' appeal. Much to his dismay, he found an entry for himself in the trope.
Ask That Guy with the Glasses is obviously more evil than those two for reasons you can find pretty much everywhere, but he had a terrible childhood, is violently fucked up, and you kind have to feel sorry for him when he breaks down in tears for no reason. Then it gets worse when he takes his medicine, and becomes the hysterical but skin-crawlingly creepy persona. It's the better alternative than the horrible, miserable wreck of a man he'd be otherwise.
Quite a few specimens fall into this and other Woobie categories... To the point that it's been put up on the "Cliches to avoid unless you SERIOUSLY know what you're doing" list. Especially if "but is really a sad person inside coping by being overly cheery" is their only flaw.
Esau from Stray, who could be described as Adamska's Evil Counterpart. He's a Tykebomb agent of the Patriots who initially comes across as a Smug Snake and does some rather cruel things in his efforts against the protagonists, but his back story is deeply unhappy. And in true Metal Gear villain fashion, his death scene is played for tragedy.
Tales of MU is narrated by one of these, especially with regards to the prejudice and bigotry of which she is routinely the victim, but which she also routinely exhibits to others. To be fair, much of this was taught to her as she grew up by her Knight Templar grandmother. But between the Mechans, the Arkhanites, Winnie, and just about anyone who disagrees with her, she gives as good as she gets on the Jerkass front.
Toki, she started out as this in Time Heals No Wounds II, before her redemption and change of heart. To further drive the point home, she wasn't always like that and was rather sweet, however, deep within the pain from being abused and then neglected (on top of that almost dying of cancer, after it was allowed to reach later stages) eventually poisoned her, allowing her personality to be tainted and turning her into the mentally ill intimidating wreck that she is, making sure no one could ever hurt her again and that she would be one to hurt, in control, and to be betray, just like it had happened to her. The quote below is just a summmary:
Brownie: Toki was once a sweet shy innocent girl who only wanted to be loved, according to Jinx and Spin, but the birth of Frailine turned her shallow, cold, cruel, dominating, calculating, and worst of all, sadistic.
From Ultra Fast Pony, Rainbow Dash. She has an obnoxious personality and likes to gloat about breaking other ponies' stuff. ("Like, OMC, I totally wrecked your house, and I'm not even gonna apologize!") She's also an orphan with a Hilariously Abusive Childhood, and she wants a real family more than anything else. Other characters even note that they're (briefly) torn over how to feel towards Dash:
Rainbow Dash: I just want to be loved for once at the gala. The Choir: No pony likes Rainbow Dash / Because she is annoying / But now I kind of pity her / No wait, the feeling has passed.
Bitch of Worm has a Hair-Trigger Temper and has maimed and even killed people, but she had an extremely harsh upbringing; her Traumatic Superpower Awakening happened when her emotionally abusive foster mother tried to drown her dog. On top of that, her powers make her unable to interpret human social cues, which left her with No Social Skills. Her Interlude makes it clear that she's very lonely, but doesn't know how to relate to people and acts aggressively because she can't tell whether or not they're mocking her.