"I care a great deal about my clients so I overwork myself at times to make sure they are happy. I could also rely more on my customer care teams to handle tasks related to package deals which I typically do because I like to ensure everything goes right."

This could be an uncomfortable question to answer and that is exactly why the interviewer has asked it, they want to put you on the spot and see how you handle it! Weaknesses are negatives and you never want to show a potential employer the chinks in your armor but there they are asking you to tell them your failings. Approach this head on. Answer this question honestly because everyone have flaws but turn it to your advantage by relating something a little on a level ground and not necessarily relating to the job. This shows that you can highlight a weakness but impress on the interviewer that you are taking great pains to overcome this. rather than saying you have a fear of flying, which of course would be detrimental to working in a travel agency; you could say that you have also wanted to play the violin but you are annoying the neighbors so you are actively looking to take some lessons! That shows a weakness but it also shows a strength as you are prepared to rectify the problem.