Pitbull Dates Puppy

So, you've got a Badass, Jerk with a Heart of Gold, an Action Girl, perhaps a Deadpan Snarker, Sociopathic Hero, Comedic Sociopath, or Tsundere (type A, though type B can also qualify) character, who normally goes for romantic interests who are similar in character.

But...is she really going out with the Non-Action Guy now?!

The opposite of All Girls Want Bad Boys / All Amazons Want Hercules, this is when someone (usually a girl or woman) who's tough, Not Good with People, often has a sarcastic sense of humor, and normally dates someone who can stand up to him/her, instead goes for The Woobie, Non-Action Guy, The Chick (gender flipped as the guy who's passive, but a lesbian "pitbull dates puppy" relationship can happen), or the Extreme Doormat. This is a relationship where you know it's doomed from the get-go because the passive half clearly doesn't have the stones to stand up to the aggressive half, especially when he or she is in bulldozer mode. This is usually a change from the people they usually date... but possibly not for the better.

With regards to the other partner, this is a person who either likes being run over by their Significant Other, or at least think they do, but later on isn't too happy about it. Generally strays into Love Martyr territory if the relationship goes on for too long.

Mostly done with women dating men these days. Sometimes done in historical romance novels where a Badass decides to marry some fresh young innocent thing as a change from his usual Vamp or Femme Fatale choices. May be a Romantic False Lead if done deliberately to screw with a more suitable ex.

Note: if the fellow is somewhat less Badass than his lady, but can and will still stand up to her, it's not quite this trope. So, Sam/Starbuck from Battlestar Galactica, Wash/Zoe from Firefly, and John/Aeryn from Farscape are similar, but don't make the cut here.

Contrast Best Her to Bed Her. Also see True Love Is Exceptional for when a similar Opposites Attract dynamic actually works out.

Anime and Manga

 * Char Aznable of Mobile Suit Gundam, a Badass Ace Pilot & later Chessmaster megalomaniac has a few relationships of this type. There's Lahla Sune, a sweet, demure Hindu girl (though she's also a Tyke Bomb) & later the similarily Yamato Nadeshiko-esque Nanai Miguel. Then again, he also dated borderline-psychotic Lady of War Haman Karn. Taken to the extreme in the novels, where he ultimately winds up together with a plump Girl Next Door named Margaret, who works as a secretary (which may have been the whole point, as the sort of people he usually meets through his work aren't really the kind anyone sane would want to start a family with).
 * The bloodthirsty Cute and Psycho Miyamiya from Bamboo Blade has the unassuming Gonk boy Dan for a boyfriend. (She never really demonstrates the especially violent aspects of her personality around him, however.)
 * Kanou and Ayase from Okane ga Nai, accentuated even more by their massive height difference. Their relationship is actually supposed to work out somehow but they've got a long way to go, considering that Kanou's still extremely forceful and dominant over the frail, would-rather-martyr-himself-than-harm-even-his-would-be-rapists Ayase 7 volumes in.
 * Lua and Ladd from Baccano! may have fit this trope, with Lua, by the end, almost getting up the courage to suggest that maybe she doesn't want to die by his hand.
 * Kara no Kyoukai: has a variation of this with Kokuto and Heroic Sociopath Defrosting Ice Queen Action Girl Tsungire Shiki. In one case taken to its logical extreme when Shiki once puts a knife to his throat and threatens to kill him. Eventually, it works out when she lets him be her Morality Pet.
 * Yandere Kanojo
 * Inverted in interesting ways in Neon Genesis Evangelion. At heart, Shinji and Asuka truly care about and are attracted to each other, but Shinji's extreme passivity and Asuka's similarly over-the-top aggressiveness prevent them from ever forming a real relationship.
 * In Onidere, gang leader Saya is head over heels for nerdy Tadashi.

Comics

 * In Killer Condom, bear Bob "Bladder" and Plumley, a normal sized mature man who manages to look quite like a puppy next to the incredibly hairy mountain of meat, Bob.

Film

 * Leigh Ann and Sean Tuohy from The Blind Side. However, in contrast to many examples of this trope, their relationship is happy and healthy.
 * Owen and Ouiser from Steel Magnolias. He doesn't seem to mind, though.
 * In noir film Rider on the Storm, heroine Mellie has probably never stood up to anyone, let alone her somewhat domineering and chauvinistic husband. The events of the movie manage to show that she's legitimately More Deadly Than the Male without changing any of this.
 * The central premise of the High Concept film "My Super Ex-Girlfriend" is this trope gone awry.

Literature

 * Jaded English spy James of Your Scandalous Ways resolves to marry some sweet innocent girl when he gets back home, as he's really sick of Femme Fatales. (This doesn't happen.)
 * Kethry of Valdemar- a tough mercenary sorceress whose lack of combat training is made up for by a magic sword- ends up Happily Married to Jadrek, a brilliant and learned Non-Action Guy who suffers from severe arthritis (incapacitating when they meet, later somewhat alleviated by magic).

Live Action TV

 * Veronica and Piz on Veronica Mars. If there had been a season 4, Piz would have been kicked in the teeth, hard. He got butthurt about Veronica's summer plans, for crying out loud.
 * Piz would have thankfully been gone from the series if season four had it ever gotten off the ground. Chris Lowell (the actor playing Piz) pretty much told Rob Thomas that he was done with the show at the end of the season as he had landed a better job on ABC's Grey's Anatomy spin-off Private Practice, meaning that (barring Rob Thomas recasting the character) he would have been written out during the gap between seasons.
 * Mary and Raphael on In Plain Sight. Mary treats Raph as a fuckbuddy, while he wants to marry her. He puts up with pretty much everything she (and her sister) dishes out. Even though they are technically "seeing other people" now, one can't help but think Raph would do better dating someone else who actually likes him beyond the bedroom.
 * The current season has them engaged, but Mary seems uncomfortable about it.
 * And then she broke it off...
 * Miss Piggy and Kermit of The Muppets, though this seems to be a rare long-term example of this sort of relationship working out.
 * House MD - Amber and Wilson..
 * Also subverted, in that
 * Quinn, who began as the Alpha Bitch of the series, and Finn, the Big Man on Campus who just happens to be a really Nice Guy, on Glee. Slightly subverted in that during the time they were together, they genuinely were in love with each other.
 * Genuinely in love with each other if you ignore the fact that Quinn slept with Finn's best friend and tried to pass the baby off as Finn's and Finn himself kissed Rachel while he and Quinn were still together. But yeah, they did have some sweet moments
 * She follows this up by then dating Sam Evans.
 * Also subverted with Santana and Brittany, because while Santana can be a bitch, and Brittany is an adorable Cloudcuckoolander, Brittany's pretty much the only person Santana is genuinely nice to.
 * Darlene and David's relationship on Roseanne.
 * April and Andy on Parks and Recreation. They get married, and it seems to work, probably because April is actually a softie under the snarky exterior.

Video Games

 * Metal Gear Solid - There's clearly something going on between Sniper Wolf and Otacon. While Otacon's massive crush for her is not entirely requited, she still is very fond of him. But even though she puts on a tough appearance, she's actually a Death Seeker and knows it will be only more painful for him if they get closer.
 * Another case are and  in MGS4. He is a complete loser and dork, while she's one of the toughest Action Girls in video game land, and has a rather mean temper as well. She shows no interest in him at all and constantly berates him for most of the game, until he saves her life not once but twice, after which she admits her affection for him, but is still quite mean most of the time. When he finally asks her to marry him, she refuses on the ground that in this relationship SHE has to propose to him, which he then gladly accepts.
 * In Left 4 Dead, Francis, a hot-blooded biker who enjoys fighting and stealing stuff, falls for cute little news reporter Rochelle. She reciprocates. Everyone else is thoroughly confused.
 * Implied with Rita and Estelle in Tales of Vesperia, though it gets no further than subtext. Rita's aggressive and pragmatic, whilst Estelle is noble, naive and sweet. She's also the only one who brings out Rita's softer side.
 * Rather common in BioWare RPGs, usually with a protagonist on the darker end of the Morality Meter:
 * Aggressive!Hawke with Merrill in Dragon Age 2. Interestingly enough, this can still occur down the Friendship path as easily as the Rivalry path.
 * Putting the PC in the Puppy position, Diplomatic!Hawke with Fenris.
 * Renegade!Shepard with Tali over the course of the Mass Effect series.
 * The Warden in Dragon Age: Origins can be played as a rather grim, vindictive, and aggressive character, and still get together with Alistair the perfect gentleman or Leliana the sweet former nun.
 * The Warden can also be an innocent, selfless all-around Nice Guy and get with the quasi-Token Evil Teammates, the Social Darwinist witch Morrigan and the blithe Professional Killer Zevran.

Web Comics

 * Homestuck: Deconstructed with Vriska and Tavros. Vriska's a Manipulative Bastard who crippled Tavros for a laugh as a child, and years later, continues to mess with him to try and toughen him up. It later turns out that part of the reason she's doing this is to try and invoke  In the end, Vriska finally winds up
 * However, her relationship with John reconstructs the trope, mostly because she's learned from her past experiences "helping" people. Not only does she succeed with him in every way she failed with Tavros, but she actually starts wanting to be a better person as a result.
 * Parodied in Hark! A Vagrant's "Strong Female Characters" story, where Susan B. Assthony becomes enticed by the "incredibly weak male lead" character, and apparently marries him.

Western Animation

 * Ka Blam!'s Henry and June. June is a hot-tempered, deadpan, tough, bossy girl with a crush on Henry, who isn't that strong or smart.
 * Janet Barch and Timothy O'Neill on Daria. A man-hating divorcee and borderline Straw Feminist falls for, dates, and  a shy, neurotic, utterly inoffensive Hippie Teacher after O'Neill gives her an impromptu therapy session about venting her feelings over being divorced.
 * Jimmy Two-Shoes and Heloise, though here it's more "Pitbull Courts Puppy", since Jimmy hasn't figured it out.