I had the same problem, when my youngest was 4. She barely ate anything, and she was small to begin with. When I spoke to my doctor about it, he said she was healthy and she was eating enough to stay that way. He said kids go through phases where they may do things that seem odd to us, but to them it's perfectly normal. He asked me if I wanted to be force-fed, "No, of course not", "Well kids don't either", was his response.
So, we started letting her fix her own plate at the table. This was one way for us to sit back and observe, what and how much SHE wanted to eat. And we were surprised that she actually was eating more than we thought. She just didn't eat a regular plate, full of food. But she ate what SHE wanted and we quit worrying so much.
Later on her appetite picked back up and she ate more. She was fine and we didn't have to fuss or nag, which was a good thing. This kid is now 25 with 3 of her own, so if my grandkids aren't always hungry, I don't make them eat a lot.
If they are hungry they will eat.
And as for him being under weight, how do you think they get the NORM?? They average the weight for 100 kids... some are average, some are more than, but some of them have to be less than, too, for them to get that AVERAGE. Of her 3, she has a tall,lean one, a shorty, and a chubby one who at 1, weighs 25 lbs. But she's just now starting to walk, so when her activity levels increase, her weight should decrease a little bit.
Just make sure there are healthy choices on the table and try to include some of his favorites a couple of times a week. Maybe let him choose whatever he wants for dinner one night each week. My kids did that for years, they each chose 1 meal each week,they helped me buy the things at the supermarket and would often help me cook that night. We even had breakfast for supper every now & then, waffles w/ fruit or scramled eggs with toast. It was still a healthy meal, but the main thing was, it was what they chose. That's important to kids.
I know I ran on a bit, but maybe some of it will make sense to you. I hope some of it will help you out.
Good Luck! Ruthie