Yeah I'd have to go straight for Dark Souls once more.
Your player character shows weakness by being about a tenth of the size of major opponents, about half the size of more or less regular opponents and by dying an awful lot until you can empower him/her by focussing on the part that really matters: surviving... and NEVER leaving the room you're playing in for a snack, a pee or some idle chitchat while the game is running, for it will come after you.
Also, never do such a stupid thing as putting down the gamepad while, say, looking at or pointing at a vital NPC, as your character is bound to just plain murder death kill stab poison or at the very least annoy said NPC if you're not careful, so your player character shows a severe lack of restraint and absolutely no common sense. Since NPCs will remain pissed of or dead once you've attacked them, the game will just get even harder, and being yelled at buckets of unpleasantness by folks you relied on just a moment ago just isn't a very fun experience. Sure, you can go pay the crazy guy playing Jesus up in the church tower, since he's on speaking terms with the guys that handle karma, but that would just add yet another weakness to our player character: Making mistakes and not going through with them.
Other than that, how about Bioshock? Isn't your player character the most gullible, easily manipulated ignorant little tool in the whole underwater shed?
Or how about Black Ops' main dude, he's well off his rockers - and he's been so for years.
Then there's Alice in American McGee's only title worth mentioning - she's cute and interesting and quite charming, but she's definitely quite insane.
Or take the pumpkin in Cauldron II - come on, he's a pumpkin. No legs, no arms, just the ability to bounce in a castle that enjoys having no stairs, fatal drops and lots of spooky objects that are normally inanimate intent on killing you dead, dead, dead. That's a pretty weak spot to start an adventure on.