Generally (keep in mind that this varies from school to school), you have to take a certain amount of courses in order to complete your degree. Some of these courses are used for a major (or double major), some might be used for a minor, and the rest will be used as electives (which are classes you get to choose on your own that don't contribute towards a major/minor).
Now, your school will have their own policies that state how many credits are required for a major and a minor. Obviously, you need to take more courses in a certain subject/field to complete a major than you would need to complete a minor, so a major involves more intense studying in a certain subject. If you have an equal interest in respiratory care and in psychology, why not go for a double major?
As for your concern regarding taking more classes than needed, this probably won't be the case (again, it depends on your school's requirements and policies regarding how many credits you need for a degree). If you did a major and a minor, you would most likely have some courses left over no matter what - and you would use these as electives. If you chose to double major, you would have less electives. But, in the end, you will be taking the same amount of courses no matter what. It's up to you to decide if you want most of them to contribute towards a double major, or if you want to have more electives.
A minor requires about half as many classes as a major. Most schools don't offer a minor in psychology - it's useless. You need at least a masters to do anything in the field, and you can't enter a graduate program in psychology with less than a major in psychology. Also, respiratory care isn't a major at 4-year colleges or universities - it's a tech school program.