12yr old DS is also very slim, in fact his rugby coach showed some concern when he went back after Christmas, as he looked to him, like he'd lost weight over the holiday, which he really didn't have capacity to lose. You can check a child's BMI on the NHS website, it's slightly different to adults and DS came up on the 25th centile, so small, but not actually underweight. I've just hired a nutritionist to work with him, as he does 20 hours of sport a week and he really needs to put a bit of weight on to be able to keep up with his peers.
DS is also not a big eater, even as a breastfed baby, he was more of a snacker, feeding for 5 mins at a time rather than the epic hour long sessions my friends babies were doing. Obviously DS is older than yours, but we've been told we need to up his calorie intake by about 1,000 a day to meet his energy needs for sport, as well as trying to put a bit of weight on. She has pointed out though, that children do have smaller stomachs, so the volume of food they can comfortably fit in, is much less than us as adults. Things we're doing:
Honey on his cereal.
Children specific protein shakes (under the nutritionist's direction)
Coconut water
Smoothies
Orange juice (not usually recommended, but he needs the calories)
Dried fruit/nuts
Cooked chicken pieces
Added cream in sauces
We've paid £75 for an initial consultation and plan, with follow up sessions £40 each. He is taking an interest in food for the first time and starting to understand that he needs to fuel his body properly, so that in itself, has been a positive. Maybe something to consider.