I have only limited experience with this as I purchase fertile eggs of rarer breeds to hatch, and thus have had times over the years when I am fairly certain I have experienced the results of over breeding as small breeders over utilize their stock or breed from over utilized lines.
First, infertility of eggs, or rather lack of development of fertile eggs. Chicks die in the shell or just prior to hatch.
If they do hatch, they take overly long to hatch (day 23 to 25 in one of my batches), and then are very spindly and unthrifty. (You have to sort out failed hatches from poor incubation procedures.)
Many chicks will have splayed legs and/or curled toes. You may see wry neck and wry tail crop up as vitamin deficiencies seem more pronounced and the genetics for recession kicks in.
If you pamper and tlc past the early chick stage, they often succumb to health issues from whatever....coccidiosis to mareks or some other unidentifiable cause as the immune system is suppressed as well.
It can be very frustrating.
Use solid birds, and while breed characteristics dictate father to daughter, for several generations, before siblings, those with concern for in breeding will have several lines that they cross to prevent over selection if the parent stock has too recent an ancestor already.
My limited experience and knowledge gained (as I delve into breeding my own olive eggers from several rare breeds).
Here's a good article about the process of selective breeding and when it becomes inbreeding depression.
https://scratchcradle.wordpress.com/2012/09/16/gms12-inbreeding-coefficients/
LofMc