I believe everyone has a different definition of what strength is and what weakness is. For some, asking for help might be a sign or weakness; while others would say that it is a strength because it takes humility and courage.
I agree that people gravitate toward those who exhibit their perceived definition of strength while avoiding those who they view as weak (again, according to their own interpretation of it).
I wouldn't go so far as to say that weakness is despised. There are those who see weakness as a challenge to overcome, a lesson to be learned, or an opportunity for growth.
It's all in how you look at it really.