Some people have a natural high metabolism which tends to cause them not to gain weight. Suggest eating 3 meals a day constituency with drinking high nutrient drinks - Ensure, Boost or make milkshakes (milk, fruit, and ice cream blended) or yogurt smoothies (yogurt, fruit, and ice cream blended) 3 times a day to help you gain weight slowly. You have to constantly eat and drink the shakes daily to gain weight if you have a high metabolism. Hoped that helped you.
I have been researching this alot lately for my 6 year old son, and here are some of the things I have learned.
The nutrients from your food are not being properly absorbed. This could be for MANY reasons, but I would not recommend drinking all that milk. Milk proteins can be very difficult to digest, and if your digestion is already impaired it would be very hard on your system, in fact could be the cause of your weight deficiency. Certain people lack the enzyme to break down milk protein (like my son). If anything, you could increase your eggs, especially yolks, to about 6 per week (2 eggs, 3 times per week). The reason for this is that underweight people often have lower cholesterol than they should. Do you have anxiety or easily irritated?
To boost your digestive efficiency, take a probiotic supplement every day to increase your beneficial intestinal flora. Then, to decrease negative bacteria or parasites (which would be robbing you of nutrients) take a few drops of grapefruit seed extract in water or juice and a scoop of glutamine powder to heal the intestine of inflammation. An additional digestive enzyme supplement could be helpful too. Also make sure you are getting your Omega 3s! These are general beneficial steps you can make. If you don't see a difference in a month or so you can get more specific testing done for other nutritional deficiencies. I don't know if I am allowed to name the lab we used, but the testing was helpful for us in figuring out all the stuff I just told you! Good luck!