My daughter was born 5lbs 5 oz. She was tiny as a baby, she grew normally however in her height but has always been under 5% in weight and now just at 6 years old is in the 20% for her age. Have your Dr show on the charts her height as it has gone up. Some kids just are petite genetically. I think it is wise for your Dr to investigate other causes, if she is active, healthy and growing in height it just may be she is skinny. I have a friend whos son does the same thing in a growth spurt his weight percentile goes way down as he grows upwards.
My daughter is six, she is 42 inches tall and 40 lbs. She was only 18 lbs on her second bday so she has had quite the spurt in the past few years.
Her brother on the other hand was almost 9lbs at birth, is now only three and 41 inches tall and weighs 42 lbs.
So each child grows differently.
If you don't trust your Dr then go take her to another Pediatrician and bring her growth charts with you.
My daughter can still get in some 4T shorts she has. I was always worried and the Dr kept telling me as long as she is eating well, sleeping well, growing in height and active then I shouldn't worry so much about it.
I can say once we got my daughters tonsils out and adnoids out that she gained like three pounds in a matter of six months so that may have been a factor when she was younger. I know she had sleep apnea due to enlarged adnoids and that kept her from gaining the weight she should have I believe.
She hates her brother is as big as she is and I keep explaining all kids are made differently and someday she will be glad she is petite. She hates being one of the shorter kids in class too.
I don't overfeed her to compensate as I don't want her going the other directions out of stress or her thinking she needs to gain weight. She eats well balanced meals and is very active. I don't discuss weight with her around. I think that in girls can lead to a lot of issues down the road. I just keep reminding her God made her the way she is and to be proud of it.
Get another opinion to ease your mind. If it isn't anything then just try and do what you are doing now.