You don't actually know how big the op's child is though? So how can you think he's the right side and it's her skewed view of her child's weight?
Because generally most kids these days are leaning to overweight. Their parents will still be obsessed with how much they eat, and swear they aren't overweight.
When my DD was in year 3, she came home from school asking me why she was the only one in her year that could not "make a smiley face with her tummy". The rest of the class all have enough abdominal fat to roll up and make this "smiley face"
I have had 8 year old children come round for dinner horrified that I am not cooking a pizza each, plus garlic bread and sides.
The vast majority of people do have a skewed view of weight. Most think if you can see a child's ribs they are underweight.
So it's worth asking, why does the o/p think her child is underweight? Has she had him weighed, does the GP agree, or is she going on her own version of "skinny".
Fwiw I have a child the same. They go "skinny" during a growth spurt, then even out ready for the next one. I don't feed them up or worry about it, I let them eat to appetite. It balances out in the long run. But then I don't get all this worrying over what children eat and what they don't. They eat if they're hungry.