Hey N.!
I don't think I'd worry too much, honestly. Your son sounds very much like our little boy (although maybe a little bigger than ours was at 1!). Our son is 3, almost 37 inches tall & weighs 29 pounds soaking wet. :)
He is *very* active, eats like a horse, and burns all of the calories he eats & then some. I seem to remember, around age 1, that Chase was a little pickier with what he ate. He ate oatmeal almost everyday (sometimes for more than one meal), and our pediatrician loved that. She said he'd outgrow his picky phase, and to continue offering a variety of foods. He did - he eats almost everything in sight these days!
Our doctor also said that with kids, you need to look at what they eat over a few days' time, not just at one meal or one day. Most toddlers get all of their nutritional requirements and eat what they need in that period of time, although each meal may not seem filling or like "enough." I'd say just make sure he's getting fruits, veggies & protein without a lot of extra sugar & fat and you both should be just fine!
Good luck!
J.
(mom to tiny Chase - 3)