Before entering an interview - it's important to prepare for this question. Consider weaknesses you could list that demonstrate you're self-aware but don't disqualify you as a candidate. For example, if you're applying for a role that interacts with the public, avoid listing "people skills" as a weakness. Instead consider a skill that has some crossover with your role. Next, think through the ways you have proactively worked to address that weakness. Have you attended webinars or classes? Have you identified and worked with subject matter experts amongst your peers? After you list the weakness, you must also demonstrate how you are actively working to address it.
“I am an introvert, so in large meetings, I tend to remain quiet, especially when more extroverted co-workers monopolize the conversation. A couple of coworkers, with whom I work closely, and trust their feedback, mentioned that when I do not speak up in meetings, not only does it make me look as if I never have anything worthwhile to say, but I deny others the opportunity to benefit from my ideas and insights. I had never really thought about it that way before. I have been seriously working on this weakness to become more comfortable speaking in front of large audiences. I recently offered to chair a committee to raise funds for United Way. And when I am in other meetings, before the chair moves on to another topic on the agenda, I indicate that I have something to say. It still feels a little bit uncomfortable for me to step outside my comfort zone, but I feel better knowing that I am being heard.”
The above answer works because public speaking is one of the biggest fears that people have. In fact, it ranks above going to the dentist. You have stated your weakness, but you have also provided two ways that you are working to improve. The hiring manager will see that you self-aware and honest. The response offered to the interview question, “What is your biggest weakness?” is only a guide, and therefore it is the job candidate’s responsibility to tweak the advice offered.