A few thoughts:
1. Avoid working in your weaknesses if at all possible.
2. If you can’t, then seek to become competent in your areas of weakness. You won’t become extraordinary in areas of weakness, but competence is sufficient.
3. Continue to spend the most time sharpening and harnessing your strengths. This is where your contribution will shine. As long as you are competent in your weaknesses, they won’t detract and your strengths will stand out and make an extraordinary contribution.
An example (a slightly risky one since I’m not huge into basketball, but you will get the point): Let’s say you are a basketball player and you are great at making baskets but pretty bad at getting rebounds. You need to become solid at getting rebounds when they come your way, so you don’t do harm. But your focus should be on putting yourself in a position to take shots, not get rebounds, if that’s where you make an incredible contribution.
And here’s an example of avoiding your weaknesses altogether: if you are a great quarterback, it doesn’t matter if you are terrible at defense. Don’t play defense. This is so obvious as to be completely undisputed.
Why, then, do we feel like there is some sort of virtue in focusing on our weaknesses in our work?
Seek to contribute where you can make the greatest contribution.