My 4 year old has always had a little puffiness under his eyes since birth. Is that just normal for some? Anything to worry about?

Probably normal. Generally there is quite a variation in "normals" with appearances around the eyes. Puffiness, slight pigmentary changes, eyelid asymmetries, & eyelid creases are some observations that occur & likely will change as child grows.As long as the eyes see well, move be well, and the eyelids function normally, I'd monitor. As an aside, environmental allergies may have some role in eyelid puffiness too.
Eye puffiness. Perhaps she hasn't actually had puffiness under her eyes since birth, but just for a long time. Puffiness under the eyes could be from allergies. Does she sneeze a lot or does she have chronic congestion and is constantly wiping her nose? Do other family members suffer from seasonal allergies/hay fever? You should take your daughter to see her pediatrician.