All the greatest villains in literature and cinema had a weakness that contributed to making them awesome.
Darth Vader had the love for his beloved ones, that first pushed him to embrace the dark side, and then èished him to turn against it and sacrifice his own life to protect his son's.
The Joker, in his madness, felt the need to share his beliefs with people, to guide and teach them, to the point that even when the win was certain he risked everything to open people's eyes to his truth and free them from the shackles of society he thought was binding them.
Grifis may have sacrificed all those around him, and yet his weakness is his also his own strength. His desire, his firm will to carve a place for himself in the world, is what drives him forward, and while Berserk is not over yet, I can imagine he would be willing to sacrifice even his own existence to chase his dream, that is also, at the same time, his very weakness.
Good character have weaknesses as well, weaknesses that frequently spell their doom. From Sturm's righteousness to Boromir's love for his country, pain for the past and desire to build a safe world with his own hands. From Ned Stark's honesty, ingenuity and moral integrity to Obi Wan's love for his pupils.
All great characters have flaws. All have weaknesses that make them memorable. That is what we are asking for. One of the worst things with application characters is to have someone get too attached and lose the will to take risks. That's what we are asking for with weaknesses. To show us that you are willing to let it go when the time is right. Can you imagine what would have happened to Star Wars if Anakin hadn't turned against the Emperor? Or to Batman if the Joker had simply put a bullet in Bruce's head without desperately trying, at every step, to connect with him? What would have happened to his epic "you complete me"? Because a weakness is the best way that your enemies have to interact with you. When it is found out, when the flaws of your character are discovered, that is the best commendation you can receive. When someone takes the time to investigate the PC you play, to look behind the curtain and see what makes him tick. When someone spends his own time in the effort to go beyond the two-dimensional pixels, and see the character you are playing.
I cannot imagine a better ending to a story I am telling than to have someone exploit my weakness. That is what we ask in application. Because we can. But I invite everyone to consider weaknesses and flaws, because they add another dimension to the storytelling.