Olivia, when she eats, do you feed her or eat with her? If it's the former, try eating together.
Some kids get their appetite to eat when they see the grownups eating too, just like my little girl. She eats what we're eating, which just means we have to watch what WE eat! Hehe. For a 10mo, somehow she knows if we're giving her baby food and she won't eat.
Also, maybe she's underweight because she has high metabolism?