The negative questions are always hard in any interview, but saying you don't have any weaknesses would be dishonest and if you don't recognize them, how can you work to make them better?
The way I've been taught to deal with this is to pick a weakness and say how you work on it and try to turn it into a positive.
Examples: Intense = focused and goal oriented
Slow = careful and thoughtful
Stubborn = pesistent and confident
Overly detailed = careful and thorough
Perfectionist = accurate, methodical, and careful
If you are stubborn and realize it, you can also identify when you are just being stubborn and and let it go, if there isn't a reason to stick to it.
Most pilots are like this. We set 2 alarms when we really need to wake up, we double check everything and triple check anything that is unusual. It's the reason we are good pilots, but we also need to recognize that it can get out of hand.
You just have to pick a 'weakness' that applies to you, turn it to a positive and come up with a situation that supports the positive spin.
Hope this helps. Good Luck!