Red vs. Blue: Church. Oh, so much. He's the universe's Butt-Monkey, but he's also a complete jerk to everyone, so you can't help but feel sorry for him and laugh at him simultaneously.
Turned Up to Eleven after season six when you learn about his torture at the hands of the Director, which drove him to insanity.
Agent Tex, to a lesser extent. She's got a frequent habit of backstabbing the Blues (though this is mostly Played for Laughs), and during her time at Project Freelancer she was an antisocial jerkass (albeit with a softer side). But after an operation to retrive the armour of CT goes wrong, she discovers the fact that she is an AI, not a real human being, then tries rescuing the Alpha but can't help him because he's too broken to come along with her, before being chased away by Sigma, who has now taken over Maine's mind. After this, she gets killed by Donut, loses one of her few friends left from her Freelancer days (York, if you must know), then gets wiped out by an EMP unit, brought Back from the Dead involuntarily, fails to discover what her purpose in life is, loses a fight to the Big Bad Duumvirate of Season 8 because she's always doomed to fail, then gets wiped from existence.
Towards the end of Season 10, Bigger Bad the Director starts growing shades of this. He's always been quite the Jerkass, but then you finally see him in the present. He endlessly watches the last video of his dead girlfriend, who he has been trying since her death to rebuild. The most significant copy of which rebelled against him and destroyed everything he had built. He also learns that his daughter has been relentlessly hunting him with the intent of murdering him for his crimes. Plus the epic Shut Up, Hannibal! by fellow Jerkass Woobie / torture victim Church about everything horrible he has done. And then it's almost 100% certain he was Driven to Suicide immediately afterwards. Yikes. Can't help but feel sorry for the guy, despite all the horrible things he's done.
Flippy from Happy Tree Friends. He's an adorable bear who suffers from severe post-traumatic stress disorder due to his time in war. While his "good" side tends to be one of the kinder and more sociable of the Tree Friends (aside from moments of cannibalism), his "evil" side will emerge whenever he sees or hears something that reminds him of war or death. Once in his evil state, he turns into an Ax-Crazy killing machine, slaughtering everyone around him in sadistic glee. One episode had him getting some therapy in an effort to overcome his disorder but the doctor was the Too Dumb to Live Lumpy who's stupidity prevented him from effectively helping Flippy. He's also just as much a Chew Toy as the rest of the cast (meaning that he tends to get killed in horribly gruesome ways if he's not the one doing the killing) and is shown looking terrified every time he comes out of his Ax-Crazy states to see the violence that he's committed against his friends.
Bitey of the Brackenwood series is one massive Jerkass, who loves nothing more than to ruin the day of the fellow inhabitants of Brackenwood. Beneath the surface however, is an intelligent creature stuck in a world of simple animals, no other Dashkin to associate with, resentment over seeing other creatures with happy families, and a simple desire to have friends.
Mackenzie, as of Episode 18. She gets her bald spot diagnosed and is especially torn when the doctor told her she's suffering from Female Pattern Baldness. She's utterly helpless when she tried to regress her anger in front of a rivaling cheer squad.
Than. Completely obnoxious, creepy, and insufferable, but it's clear he really does just want the football players to like him.
Brittnay would also count, if you feel sorry for her because her car got blown up by Mackenzie.
The entire squad (mostly sans Trisha for the Jerkass part) as of season 3. Sure, they may be giant bitches, but the New Year's Eve episode completely highlights the friendlessness the squad had going on and as of episode 40, they are so desperate for new members, they just hire anyone they know regardless of who they were.
Shay van Buren, definitely—if you side with her over the Cheerleaders. She's been through a lot of crap, when you think about it.
Qrow Branwen of RWBY. He is a bitter, grumpy alcoholic who enjoys provoking other characters and is quick to provide scathing opinions about people he doesn't like, but does care very deeply for the people he does like (particularly his two nieces). His ability to literally bring bad luck and misfortune to others around him adds to his already impressive skills as a Hunstman, but because he can't turn this ability off or control who it effects, he's forced to keep his distance from his family and few friends he does have. Add in the fact that his old team (consisting of his sister, brother-in-law, and said brother-in-law's now deceased second wife) was broken apart by the aforementioned sister, and the general Crapsack World that he lives in, and it's no wonder he's always drunk.