I don't find shy women to be weak, so I doubt most women find shy guys to be weak... In fact, I very much prefer a quiet women instead of a brazen, cocky, loud mouth. Some bold and confident people come off as arrogant to me, while many shy people just suffer from low self-esteem. A bold person should probably tone it down, but they seldom do. After a shy person gets comfortable around you, they gain confidence and have no trouble speaking their mind.. Neither scenario is particularly preferable.
Actually the opposite is true. Women are prone to find outgoing men to seem more confident, strong and better leaders than a man who is shy and quiet. The 'alpha male', so to speak. The downside is many women go for the alpha male without realizing the potential serious flaws that can come along with them.
Of course there are all generalities and not reflective of all men and women, but do seem to be a generic standard.
Typically these sorts of questions are moot. Firstly there is no black and white answer to 'does X gender like/dislike/prefer/etc this trait in Y gender'. The answer is always 'it depends on the individual'. Sure, there can be more of a predominance, but with 7.5 billion people on earth even the minority still leaves a lot of potential choices and options.
And if you are asking, chances are you reflect the trait you're asking about. And it's who you are. So regardless of the answer you aren't going to magically change into the other type. And if you tried to you would simply be faking it and being dishonest with yourself and the other person.
Be yourself. Stop worrying about finding answers to unanswerable questions to gauge your chances. If God has it for you to marry, none of these questions or concerns will matter. He will bring the right kind of person at the right time.