I want to know whether it is necessary to change the bloodline when breeding between sibling budgies (e.g. the breeding male and female pair are also brother and sister). I recently bred with a sibling pair and the resulting chick size is smaller than a normal budgie chick. When this chick grows up, will its body structure remain small? Is there any specific reason behind it?
Breeding animals is all about genetics. So, let me give you a quick, as simple as I can make it, lesson in genetics. (Disclaimer: It will be so grossly simplified that anyone who's studied genetics will probably yell at me).
You've probably heard of genes before; they're blueprints that contain the DNA passed down to children from their parents. There are also things called alleles, which produce the variations in each trait. In a very simple explanation, the genes contain the code, but the alleles decide what to do with it.
So, the parents pass down genes to their children, and then through a complicated process of gene inheritance (not a simple explanation), alleles decide which traits become dominant in the child based somewhat on the parents, and somewhat on their own. For example: if you take two people with brown hair and they have a child, that child is more likely to have brown hair, as brown hair becomes the dominant trait, but it's also possible for it to have a different color of hair based on whatever recessive traits are in its genes.
A dominant trait is simply a trait that's more likely to occur in the child, while a recessive trait is less likely. In humans, for example, red hair is a recessive trait, and because we don't breed for the sake of hair color, the chances of a child having red hair in the future will continue to shrink.
It's important to note here that not all traits are as harmless as the color of a person's hair or eyes. Passed on traits can include susceptibility to certain diseases, proneness to certain types of cancer, and various deformities. A high genetic diversity reduces the risk of the harmful traits, as healthier genes are more likely to be combined and take priority.
Here's where it becomes related to your question. When you take two people who are related to each other, and they have a child, it increases the chances for those recessive traits to become dominant, as they're apparent in both parents. What you're seeing with your chick being a smaller size than normal is actually one of the milder examples. Other cases include infertility, missing/extra limbs, miscarriages, lower mental capacity, and a loss of the immune system.
While I don't suggest it, it's a pretty common practice in the more (for lack of a better term) driven breeders to take two siblings with a certain trait they want and breed them to make that trait the dominant one. These breeders are also prepared to cull any part of the litter that has defects. Even then though, it's important that only the first generation is bred together, and further along, and the risks increase incredibly.
With all this being said, unless you're prepared to deal with any children that are born with undesirable traits, and you're aware that birds will attack a chick if they can sense it is producing an undesirable trait (especially deformities), I say that it is a necessity to keep breeding pairs of unrelated individuals.