My son is a grazers. He loves to have small amounts to munch on throughout the day. Having healthy finger foods around for him to freely eat has increased the amount he eats and he has gained healthy weight. He has always been thin, so much so that when he was in second grade and I saw him on the soccer field I thought people would think I was not feeding him properly. (I was.)
Also, we follow the Eat Right For Your Blood Type Diet. Turns out he have different foods that are beneficial and I don't even like most of his beneficials, so I wasn't working with was works for him. Once I discovered the difference and got the food lists, it was a small adjustment to include his foods in my buying habits. By introducing foods that are on the beneficial list for him (not appealing to my tastes) he eats a lot more. IE: I do well on meat and he does better w/beans, I can not eat cheese and it works just fine for him. He loves his diet and is older and quite solid now though still a naturally slim person.
Be careful of the "give him anything he'll eat" temptation. It is not worth him developing bad eating habits.
Also, remember when you put pressure on yourself or him you are going to have opposing effect - so if it worries you that he does not eat...he won't eat. It's not him its how energy works. One energy must oppose the energy that is pushing. Moving with what is happening and looking with compassion for the answer you do not create that opposing force. Worry is fear and will always be met with resistance. Compassion is not pushing, it is seeing and flowing. This is the happier female response to energy = mom's can be very good at this when we don't get caught in our worldly energy and we choose to follow our internal, maternal compassionate compass.
Provide love and support and if he really is not eating enough then get yummy vitamins for him to snack on. Foods dense in nutrition...frozen blueberries, organic licoric, carrots in ranch, nut butters etc.
Sometimes you have to push a little, in a nice way, to get your doctor to do a blood test, but there are tests that run a vitamins/mineral panel and get a good internal snap shot of any defincenties. If one lab doesn't provide it, ask your doctors office to call a lab that does. Also, you should know your child's blood type for the diet and for "just in case".
One other mom here mentioned celiacs - it is worth testing him for this now. Finding out about it now makes the rest of his life easier and healthier.
Good luck, nature doesn't always work the we "think" it should, but if we slow down and look gently there is an answer right in front of us.