Weakness is something that people (okay, men) tend to think of in one of two ways:
- Something hateful to be purged and never admitted to, or
- A challenge to be met and overcome, for that is true strength.
Both are wrong. Weakness is all you are.
Your wife doesn't love you for your strengths: she loves you for your weaknesses, your flaws, the things you need her to compensate for. Your strengths are just canvas: weaknesses are the swirls of paint that make a picture. Armour is immobile without chinks. You need your weaknesses.
That's not to say that you should just accept them, or that you shouldn't try to work around them. Any friend or lover will do so, will accommodate your flaws but still try to talk you out of them, in a faintly perverse way. But you can't usually cure a weakness without throwing away a strength. Sensitivity is a weakness and a strength, context-dependent; so is courage, so is innocence, so is immaturity, cynicism, workaholism... anything that can be exploited to hurt you by one can be what makes another love you.
It's a dreadfully self-help-book thing to say, but you can gain a lot by writing your weaknesses down on one side of a notepad, and their concomitant strengths opposite. It's something I do with characters all the time, after I've decided what they drink and who would play them in the movie, of course.
But with other people, you have to strike a balance. You have to accept their weaknesses, but you don't have to accept their decisions. You can't punish someone for what they are, only for what they do.