Our son (aged 5.5 years old) is another lightweight. He has not gained much weight in the last year, but has shot up in height by over 3". He is healthy (had his first sniffles this past Winter that lasted two days!), and seems to live on AIR! The other day, he weighed himself and was at 38#. He's been that same weight ((+ or - lb)) for a year.
We measured him last week, and he actually grew 1" in the last month!!!
He is not a big eater. Like you, we give him free rein on whatever he wants. He will only eat very small portions of even his favorite foods. This is a child that will never stuff himself on anything! Even things like chocolate or other sweets. He'll take a couple of bites of a candy bar, and put the rest of it away in the fridge to eat later. ((This drives me crazy, as I do not have that kind of will power!!))
I have quit worrying about this. He is developing at an incredible rate mentally & emotionally. Physically, he is just a lightweight, not unhealthy. I'd rather he be picky and slender, than having a chunky child.
I took him to a well-child visit with a new physician ((we don't vax and we finally found a doc that respects this, and just wanted to get aquainted. It was the only well-child visit we'll be doing)) and that doc said not to worry about him, he's developing just fine, and he asked about what my husband's build is like instead. Dh is 6'5" and 200 slender pounds. I am 5'2" and 105. So, our son is just taking after us. He said, "Go home and worry about things other G. He's just fine!"
So, we did!!!
As regards you child, I wouldn't worry if she is healthy and normal in her other development. Did the health care worker seem concerned? I'd say look at your daughter's genetic make-up, and base your assessment on THAT. If everyone in both sides of the family are on the slender side, then she is just following suit!