HI,
Eggs are high in protein and too much of it can cause diarrhoea in kids. But I do not think there is any other reason that you should worry about as now studies say that eggs do not have bad choleserol and are good.
But as they say, "Excess of everything is bad." So, do not give too much of eggs as there would be other things high in protein that you must be feeding your child each day. Please go through the article.
http://www.news.com.au/lifestyle/health/diet/how-much-do-children-actually-need-to-eat/news-story/4f3a8f49ccf7e62573e36fec0cf1ceb5
Sweta Ghosh