Don't use checkboxes. It's so rubbish.

I would try to split it into two questions:

1. In the last 3 years, have you had any nasty illnesses?
   ○ yes
   ○ no

2. Which ones?
   ○ headaches
   ○ colds
   ○ flu
   ○ arthritis
   etc.

Only show question 2 once they answer "yes" to question 1.

The drawback is that the user might have had a disease which isn't on your list, so they would choose "yes", and then ... be flummoxed as to what to answer for question 2.

In which case, perhaps you could add a final (catch-all) "other" option to question 2. Maybe your business logic doesn't allow for that, I don't know.

Don't use checkboxes.

I would try to split it into two questions:

1. In the last 3 years, have you had any nasty illnesses?
   ○ yes
   ○ no

2. Which ones?
   ○ headaches
   ○ colds
   ○ flu
   ○ arthritis
   etc.

Only show question 2 once they answer "yes" to question 1.

The drawback is that the user might have had a disease which isn't on your list, so they would choose "yes", and then ... be flummoxed as to what to answer for question 2.

In which case, perhaps you could add a final (catch-all) "other" option to question 2. Maybe your business logic doesn't allow for that, I don't know.