A place to talk about parenting.
Be respectful of others' parenting decisions.
BMI is generally a shitty indicator. I had 16 at some (rather long) point in my life, and now, I... let's say, don't. If his blood tests are fine and he's functioning well, I'd let nature run its course, especially if he's eating well. Pushing empty calories into him is just going to create food intake disorders.
—a person who's been in somewhat a similar situation and who's around several people with food intake disorders and a father to a very skinny kid presumably without one
My parents tried to get me to gain weight my entire life. It led to a pretty bad diet by the time I was living on my own and I only ever gained weight when I ate chicken burgers from meal hall literally every day.
Don't focus on weight, just make sure he is healthy. It can lead to poor choices and insecurities down the road.
That is my fear, honestly. He is a great fruit eater and a pretty decent veggie eater, especially compared to his peers. My once-skinny husband never was and he has definitely put on weight in adulthood (although I’m also not one to talk, but at least I eat fruits and veggies; I just also have an insatiable sweet tooth). He eats some junk food but I worry less about that when, if given the option, he’d likely choose salmon sushi and strawberries over almost anything else that might be offered.
Then that's great! Don't let anyone shame him for being skinny unless there are pressing health consequences.
Honestly, an athletic kid, you just make sure their protein intake keeps up with their activity and don't worry much about weight until and unless the doctor says it's a problem.
Your post and comments are kinda confusing in that regard, but it seems like the doctor isn't worried about it, everything relevant has been checked and that this is a more general concern from your side. If that's not the case, you could consult with a nutritionist and see what kind of dietary changes might better support the kid's activity levels.
But, usually, it's only weight loss that's going to be a problem as long as growth is still ongoing
She is a bit worried. She did say it’s good that he’s not losing weight. But she is concerned that he’s not gaining at a rate that is on pace with his height.
If that's the case, gotta work in a well rounded workout diet. At 10 (or did I misread?), he's not going to pack on a ton of muscle, but he won't put any on without the diet being balanced for the amount of work he's putting in, even at kiddie karate level of output. If the classes are more serious, the workout they give will be too.
If you can't get advice from a nutritionist, just up the protein a little at a time until he either starts gaining lean weight, or it becomes evident that his body just isn't ready to gain that kind of mass yet.
Just track what he's getting, and bump it up as needed, with the goal being (and this is general purpose, without knowing the kid or any medical history, so definitely triple check) in the 35 to 40 grams per day range. That's just a tiny bit above the typically recommend levels for his age, but should be enough to notice change in a week or two.
You could likely go as high as 50 grams a day, though for sure talk to the doctor again before staying at that range. The increased protein intake shifts how a kid's body handles calorie management, and I'm simply not up to date on the whole subject. Only reason I have recent enough info to merit commenting is having taught some kids in that age range some martial arts over the last couple of years.
Again, you gotta take internet advice with a grain of salt. No matter how well intended, no matter how well informed, we just don't have the full medical breakdown, or any direct interaction with the lad to be certain of much of what we can say.
Only other thing I'd throw in is the general advice to not push beyond his appetite often. Sometimes, it's necessary, but when it's frequent, kids tend to adapt too well, and get focused on the wrong aspect. That can lead to over eating regularly. When they keep pushing past satiety, they can lose sensitivity to satiety to some degree or another. I tend to err on the side of offering things more often rather than increasing amounts per sitting.