This is a question that is always asked during an interview. The interviewer will ask it to see how you answer it. It really has less to do with the answer and more on your demeanor and answer substance. Answer substance is important because it shows how professional you can be while answering a question which there really isn’t a right or wrong answer for.
When answering this question, make the answer reflective on your person in a good way. Such as, you can have a professional weakness for giving people second chances to prove their worth. This shows that you have empathy and the ability to work with difficult people. A professional weakness doesn’t have to be a negative reflection of you. The idea for mastering this question is learning how to answer a “seeming” negative question with a positive answer. Another example is, have a professional weakness for staying late at work when told to go home because you feel the priority of a project is so important to the success of the company.
It sounds corny, but these are actual answers I have used and in some cases I was offered the job right there on the spot based on my answers. Think about this question and have some rehearsed answers, all the best to you.