Welcome to the beyondblue forum. This sounds like a tough situation and there are a lot of topics about helping someone you care about with their mental health. You boyfriends insecurities or anxiety is something that he will likely need to take charge of and find some solutions and strategies. I fear that if you just stop going clubbing, the same feelings he has may resurface in another activity that you do without him and all of sudden you are changing your life to work around his worry but his anxiety isn't improving.
I wonder if your partner would be receptive to learning about his worry and taking some steps towards better understanding and managing his symptoms? There are several programs and solutions that are available such as an online program called Mindspot that is for people with low mood and worry symptoms (18 years or older) as a program called headspace which is available across Australia (12- 25 years old). This depends on whether you boyfriend is willing to talk with any one. Another step might be to see if your boyfriend would go and visit a GP and discuss his worry with a doctor who can make some recommendations. Often people who have worry don't feel sick enough to go to a doctor but the truth is, the earlier symptoms are caught and managed, the easier and faster they resolve.
In your case, you may benefit from talking with someone about setting goals and boundaries for yourself in your relationship. You might visit your GP or even talk with a friend or someone your trust. You will also get some responses on the forum or find similar threads about supporting loved ones with anxiety as this is not an uncommon situation. Here are a few links to get you started in the right direction.
Wishing you the best possible outcome,