How should I give a talk about my paper if I know it has a significant weakness?
How should you talk about the weakness? Honestly.
This doesn't mean you need to dwell on it or undermine all the rest of this talk around your point. But if you know about a serious weakness, you shouldn't be afraid to acknowledge it when necessary.
Yes, your work will appear less awesome as a result. But which of these two scenarios would you rather have?
- You show the work you did, acknowledge the weakness, and discuss how you think it would be best to improve the work in the future in order to achieve the overall goals. You haven't solved the problem, but you've taken a useful step.
- You claim your work has no weaknesses, and when people inevitably notice, they think that you are either too foolish to notice the weakness or too insecure and self-important to acknowledge it.
Your paper was accepted, despite the reviewers pointing out the weakness, and that means people must find something of value in it. Focus on the value that is still there despite the weakness, and let that be the point on which you build.
Too long for a comment, so I'm posting as an answer:
Not meaning to be offensive, but it sounds like your advisor is not the most ethical of academics and is leading you astray. If the "question" that seems to be asked by "everyone" is highly relevant to the quality of the work, and yet doesn't have a satisfactory answer, then that fact should not have been hidden or glossed over just to get acceptance for the paper.
Now you're sort of in a bind. The best way out of this is to attack the situation head-on and be fully prepared to talk about that very thing as a significant limitation to your work, maybe even pre-emptively. Many papers freely discuss their limitations in the text, and this is considered a hallmark of intellectual honesty.
Remember, your academic reputation is very much on the line, along with that of your advisor.
You may discuss the problem as a topic for future study.