From your measurements he is underweight for his height. If you want additional tests, then ask your Doctor, Ketosis is when the body does not have enough glucose (food) and it starts breaking down fat and protein; and ketones are the by-products which can become a dangerous state if too high. 2800-3000 calories is what he should eat. Try to eat a Heart Healthy diet which will give you the nutrients, vitamins and minerals your body needs, not strain the heart with too much fat, and help with possibly preventing future disease states. Heart Healthy diet which is a moderate fat diet and a moderate fat diet means = using polyunsaturated (omega 3, corn oil, nuts, etc) fats and monounsaturated (olive oil, canola oil, peanut oil, etc) fats, no saturated fats (high fat snack foods, butter, fat spreads) and no trans fats. Eat low fat meats (chicken, fish, loin of pork) or non-meat sources (soy products, nuts), low fat vegetarian combinations (rice & beans, pasta & beans, low fat cheese & pasta), low fat and substitute dairy products (1% milk, low fat/fat free yogurts, low fat soy milk/soy yogurt), use plant oils, non trans-fat margarines, and eat a lot of fruits and vegetables. Eat daily high fiber breads and cereals (oatmeal). Try nutrient dense drinks 1-2 a day, either purchase them, such as Ensure or Boost, or make your own yogurt smoothies - yogurt, milk, and frozen fruit blended together for additional calories, protein and nutrients to help increase your weight. Hoped that helped you.