When it comes to our professional development, weaknesses usually get a bad rep. Feedback to subordinates or peers about weaknesses is something most love to hate. So we start the discussion with good stuff, ease into the difficult stuff - hurry up and discuss it - and then (whew) finish with more feel good stuff.
The problem with a sandwich approach (good-bad-good) is that people tend to remember the end of a story.
A different approach is to view weaknesses as an overused strength. Get your organization aligned on this belief and you'll chart a new course. If you start looking hard enough, you'll find that most - if not all - weaknesses can be explained as such.
For example, Tom's weakness is not being down to earth or focusing on what can actually be done. This is likely a result of Tom being very strong in conceptual or big picture thinking - which is a good thing to have. Teaching Tom to understand when it is being overused can be an effective way to improve his behavior.
Jill's weakness on the other hand is being too rigid and not wanting to consider new ideas, especially at the last minute. This is likely a result of Jill being very reliable and good at complying with process. Teaching Jill when her strengths are being overused is key to helping her be her best.
Approaching weaknesses as an overused strength helps remind us it's something we must be mindful of daily. It also helps us accept the feedback because we see it comes from something good.