What is meant by "He (or she) has a weak character"?

In my last few years of working in the NHS as a nurse manager the catch phrase was 'resilience'. Staff and people being interviewed for jobs were being tested all the time for their resilience - in short their ability to take all the * that was being thrown at them on a daily basis without crumbling.

I think the idea of some people having weak characters has rather gone out of fashion, even to the extent of having a strong character being perhaps a bad thing, in the sense that people are sometimes said to be strong characters, when what is meant is that they say what they think without consideration of how it impacts on others, or do what they like irrespective of others' wishes.

To me, a weak character would be someone who is easily led and influenced into doing things that are wrong and that they know to be wrong, for no other reason than someone else has persuaded them to do it.
As my mother used to say, 'would you go and jump off a cliff just because so-and-so told you to do it?' whenever I used the fact that a friend had told me to do something as an excuse for bad behaviour!