M.S.
K., It sounds like you have two problems: your son doesn't like to eat; and your son doesn't like to feed himself. What a quandary for you! My son (26 months and also underweight, in fact has LOST weight) won't let us feed him (so I can't help you in this area), but he also does not really like to eat. It's not even that I would classify him as "picky". He just is hit and miss about food. I would recommend reading "what to expect the toddler years" for some great advice about the parent/toddler relationship regarding food. First and foremost, I had to back off. Don't praise eating, don't encourage eating, stop making a big deal out of it, when he says he's done, let him be done. Eat dinner as a family as often as you can. I was amazed at how much all this helped!!! Other things that helped were: compartment plates (silly, but true), offering smaller amounts of food, always offering at least one thing I know my son will eat, not giving into the "I want ____ instead" request. He gets what he's been given. Don't tie up rewards with eating. You either provide dessert or you don't. If our son wants more of something, we ask him to take a bite of something else on his plate first. He NEVER has to try something he doesn't want to try. When we took the battle out of mealtime, his habits improved drastically.
All that said...I second the allergy hunt idea. For other reasons (ear infections), we took our son off dairy as an experiement, about 8 weeks ago. Not only did he start sleeping 2 hours longer at night and his eczema cleared up substantially, but he changed the way he ate...he stopped requesting banana after banana (2 or 3 a day!) and started trying more veges, also started to eat meat, which we'd never seen him do!! I know it's hard to watch your underweight child really struggle with food. I wish you luck.