"I am gratified to see the progress that many have made in the health reform, yet am sorry to see so many behind. If any become sick upon our encampments, inquiry should be made as to the cause, and note should be taken of the case. I am not willing that the reputation of our camp meetings should suffer by their being reported as the cause of making people sick. If a proper course be pursued at these important gatherings, they can be made a blessing to the bodily health as well as to the health of the soul. 2T 603.2"
"Beloved, I wish above all things that thou mayest prosper and be in health, even as thy soul prospereth."
Both passages express a desire for both physical and spiritual health. 3 John 1:2 is a direct wish for prosperity and health as the soul prospers, while the EGW passage hopes the camp meetings will be a blessing to both bodily and spiritual health.
"For this cause many are weak and sickly among you, and many sleep."
Both passages connect sickness with a cause. In 1 Corinthians, it's related to improper observance of the Lord's Supper. In EGW, it's related to neglecting health principles at camp meetings. Both suggest a link between spiritual/moral failings and physical health.