Jerkass Woobie/Web Original

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.)
Esau from Stray, who could be described as Adamska's Evil Counterpart. He's a Tyke Bomb 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 Solid villain fashion, his death scene is played for tragedy.
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 Nostalgia Critic. He acts like a brat, often goes annoyingly screechy when pissy, and fights with everyone. But he suffers so much from the movies he watches, gets walked all over at least once by everyone on the site, and is a good guy at heart. Taken Up to Eleven in fanfiction where he's the fandom bike, and they tend to do their very best to break him by humiliating him as much as they can.
- Perhaps fittingly, The Nostalgia Chick too. She's not too fond of empathy, treats BFF Nella like crap (even though Nella is a Butt Monkey professionally, it still counts), and her reasons for killing the Critic in Kickassia was purely for her own gain and has nothing to do with the others. However, she has awful self-esteem, had a shitty childhood, and there's been a few times where you can tell that she really does love her best friend.
- 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.
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.
Captain Hammer, by the end of Dr. Horrible's Sing-Along Blog. He's a Jerk Jock who bullies the Villain Protagonist For the Evulz, and is only a hero because it's easier and it gets him laid. Then, at the end, we find out that, in his entire life, he's never before felt pain, and when he does, his response is to cry for his mother and run away.
- The aforementioned Villain Protagonist - Doctor Horrible himself - counts as well. Too nervous around the women he's attracted to to tell her that he likes her, gets brutally beaten up by Captain Hammer repeatedly, but he is still a Card-Carrying Villain (not to mention his feelings for Penny can be interpreted in a less sympathetic way).
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.
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.
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.
If you stretch the definition of "Woobie" quite a bit, and keep in mind that "Jerkass" is a gross understatement, SCP-682 could be interpreted as one.