The word “spirit” here refers to the energy of a person. It is your will and ability to do things. When your spirit is revived, you become active (see e.g., Genesis 45:27). But here David says that his spirit faints, he feels very weak and is ready to give up. His energy is gone. This also affects your body. When you feel so depressed, you start to feel physically miserable.
3 When my spirit faints within me, you know my way! In the path where I walk they have hidden a trap for me.