How do brown eggs become brown (instead of white)?
The brown color in an egg is laid on in the chicken's reproductive tract by the shell gland pouch. Some breeds lay a tinted egg with a very light brown color, and some breeds lay extremely dark chocolate brown eggs. The breeds just produce more or less of the brown color that goes on the shell.
Interestingly, individual hens--while they lay basically the same color throughout their lives--will still start out laying darker eggs at the beginning of the season after their bodies have had a (winter) break. When they hit their egg-laying stride, laying as quickly as they can for their breed, often their eggs lighten up. Heat stress can also cause eggs to lighten. And as they lay at a faster and faster rate and their eggs get larger, the hens themselves also lighten. There is only a certain amount of color each hen produces. If it is laid over more eggs or over a larger surface area, the eggs will be a lighter color.
Even the egg color of dark brown layers will naturally vary in intensity over the course of the season. The eggs of Marans can go from chocolate to not much darker than the egg of a regular brown layer. After a break in laying such as a molt (or a period of broodiness), the eggs will become darker again.