Pullets usually start laying small eggs that will gradually get larger as they keep laying (not counting the occasional odd double egg) and hit full size after a couple of months or so depending on the breed. Some types, like sex-links or White Leghorns strictly bred for egg production will just always lay bigger eggs. After their first molt when they start laying again, those are usually the largest their eggs will be, and they will keep laying about that size until they get old.
Shell color is not related to feather color. They think there are like 13 genes that control brown egg color in general. Brown eggs are initially white, and the brown shell color comes from the various pigments the hen deposits on the egg, protoporphyrin-IX mostly in the commercial brown egg layers, they derive it from haemoglobin in their blood.
