Many people, including myself, added or will add a candle on Friday night for each child that is born. Where and when did this custom originate?
The oldest source I could find is the Likutei MaHarich - (c. 1900). I recall hearing that the custom started, since the Halacha is that if the lady forgot to light one week she has to add a candle in future weeks, often when a lady gave birth they were busy and forgot. (Childbirth was not as easy years ago). Due to this they added a candle and today it has become a common Minhag.
It is a new development, adopted mostly among Hassidim and Hungarian Jews. Seems to have become more widespread in past century.
Nowadays people are relatively affluent and can afford it more than in the past.
However, the old minhag is to light just two.
Lighting additional ones, especially many, can increase hazards of the flames, especially when there are children around, and also obscures the symbolism of two lights corresponding to Zachor and Shamor that the old codes of halachah cite. Therefore careful people stick to the tradition of the old minhag and reject this new development.
More isn't always better. Sometimes more is less.