Hmmmm.... My DD has eggs nearly everyday. It is a great brekkie and she actually eats them (she is pretty fussy). The general guideline in North America on eggs in 3-4 yolks a week for healthy adults.
I have egg whites - generally Eggbeaters - DD will eats these as well, if you are worried about cholesterol this is a good option no cholesterol and full of protein.
Is Charlie still on whole milk? One of the main reasons I moved Sophie to 2% is because she eats eggs a lot. If you cut some saturated fat and cholesterol, processed meats, cheese, butter, yogurts, red meats, from other areas of his diet I would think he could have eggs more often.
HTH