My daughter weighed the same at 12 months and her doctors were concerned. One inexperienced doctor suggested testing for celiac disease, but our regular ped disagreed and said she would probably catch up in her second year. He wanted me to feed her Pediasure, but she hated it. I kept nursing and offered as much high-calorie food as I could. This included:
-organic butter on pasta and melted into cooked vegetables
-organic cream and maple syrup in her oatmeal
-avocadoes (usually as homemade guacamole)
-whole milk yogurt and Kefir (she would not drink milk)
-cheese sticks and other forms of cheese
-organic eggs - she would eat 2 yolks in one sitting!
-meatballs, cut-up chicken and steak, canned beans
-gluten-free cookies (in case gluten was an issue)
They also tested every 6 months for lead and anemia. She was borderline anemic at times.
By 18 months she only weighed 19.5 pounds, but after stressing about all the calories, at her 2 year check up, she was 23.5 lbs! Back on the growth chart and looking good! She was always a voracious eater, which is part of the reason we didn't worry so much. My husband and I were also small/skinny kids and relatively short adults.
If your son isn't wanting to eat, that may require some follow up. But otherwise, expect him to catch up in year 2 if you are feeding him healthy, high-calorie foods. If you are nursing, don't wean until you are sure he'll drink cow's milk. Good luck!