The shell must be strong enough to support the egg’s weight and protect the embryo, but thin enough for the chick to break through when hatching.
As size increases, the weight grows cubically (volume), but shell strength only increases quadratically (surface area), so there’s a point where the shell would have to be too thick to hatch from.
The distance from the shell to the center increases.
Oxygen diffusion becomes inefficient, and the embryo could suffocate.
Larger eggs are harder to keep at a uniform temperature.
Birds incubating the eggs would need to generate and distribute more heat, which is physically demanding.
Here is what I found: