Here is what I found:

• 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.