Hi Carney and welcome to the forums,
You are right in thinking that your budgie's health will be affected by these successive breedings. The health of any incoming chicks will suffer the consequences as well because most likely your pair, especially the female is already in a weakened state from laying and raising multiple clutches in a row.
With so many eggs laid in a short amount of time, your budgie's calcium levels must be low at this point and the risks of her becoming egg bound are higher too.
You need to separate your female budgie from her mate and place her alone into a spare cage in order to help breaking the egg laying cycle and make her come out of breeding condition.
Do not give your budgie anything that she can use as a nest and this includes open food containers. You can get a different style of food container that has a top on with a small opening where only the head will fit in for feeding purposes.
All nest boxes, hiding spots and potential nesting areas must be removed from all cages in order to discourage breeding.
For detailed information you can check this link: https://talkbudgies.com/budgie-breedi...want-eggs.html
Have you kept all of your pair's chicks? If so, then you must take strict measures in order to prevent inbreeding once they get older.
It would be a good idea to house the siblings by gender, sisters in one cage and brothers in another cage.
Your pair needs a really good rest from breeding, in fact from your description and the fact that your female budgie seems to be quite determined in laying eggs and raising clutches, there is the chance that she may be a chronic egg layer and it's not advisable to breed from chronic egg laying hens. Not only their health is put at risk but also this less than desirable trait can be passed to the female offspring.
Best of luck in getting your budgie out of the breeding mood.