Weak Characters

I was asked the question, what do you do with weak characters? As I have thought on the question I've found myself stumped.

We've all seen them, those characters who are a part of the story but have no backbone, they have a desire to join in but their ultimate end goal is unachievable because of their willingness to do whatever anyone else tells them to do.  They want to be a part of the action, they want to participate in the action but they are far too weak to do so; the question arises in the mind of the author what do you do with these characters?  Can a weak character be written in such a way that they don't turn into a minion?  Can they be incorporated into the story without making them annoying?  My answer? Maybe.

A character can always learn to not be weak, they can become physically stronger through training, cyborg parts, ninja school, whatever depending on your genre.  However, how does one make a mentally weak person stronger? There is the age old remedy of give them struggles until they overcome, let them suffer mercilessly until they either bend or break.  The problem is that if you've ever been a writer you will understand that until you spend time inside a character's head it is hard to know if they would even change.  You can write the greatest character in the world thinking they'll achieve greatness but when you spend time inside of their head and suddenly discover they're mentally weak, incapable of changing their desires because they can't seem to let go of the need to please someone else.  Suddenly you're faced with a conflict, do you keep the character and force change, which betrays the character in every way, or do you let them go on fluttering in the wind?

It's hard to know what do with those characters because, just as in real life, if someone isn't willing to grow a back bone they're always going to subject themselves to the stronger willed and giving up their own desires to please someone else.  So I ask the question what do you do with those characters?  Sometimes they serve a purpose in story telling, every story occasionally needs the mindless drone- the stormtroopers of story telling- but what do you do when the character is just there?  What do you do when they become annoying?  My knee jerk reaction is usually, "kill them".  I'm a firm believer in the strong survive the weak die and being a sci-fi/fantasy writer myself I find that methods is much more effective but how does a writer not constantly do this?  How can the weak survive, serve a purpose, and still be meaningful to the story?  I guess I don't have a good answer, so dear readers the question goes to you.  What do you do?