Your daughter appears to be eating a variety of foods, and I think your approach to limiting the snacks is appropriate even though you worry about her weight. She may just have a very high metabolism and easily burns up any extra calories she eats.
I suggest you talk to your pediatrician about your concerns to rule out any metabolic disorders. If your daughter is not anemic, and the physician feels she is healthy, I wouldn't worry about her weight. If she has always been in the fifth percentile but is not losing weight, she is probably following her own normal growth pattern. Ask the pediatrician to do a BMI (basal metabolic index). This is a better indicator for a child over 2 years of age regarding appropriate weight status.
Finally, it is important to understand that the growth charts are a guideline for growth. If they are being used properly, a child's height for age and weight for length must also be plotted. It is the weight for length that is the most important indicator because it clearly shows when a child is growing appropriately. If the parents are small, especially in height, I would expect to see a weight in the lower range of the growth chart for their children. But I would also expect to see a weight for length measurement at around the 50th percentile.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.