A chocobo egg is about 36 cm long and weighs about 20 kg.
I couldn't find any good sources on how much a chocobo weighs. It probably doesn't matter anyway, because bird to egg weight ratios vary wildly across species.
I did, however, find one clear screenshot of a chocobo egg from Type-0 and compared the egg against other objects in the shot.
The egg itself is approximately 180 pixels tall along its major axis.
The chocobo chick is 115 pixels tall. As chocobo chicks are about 17 cm tall, this works out to approximately 0.15 cm/pixel.
The character on the left stands 400 pixels at the waist. It's not clear which Type-0 protagonist he is, which puts his height anywhere between 168 and 187 cm. If his waist is about half his height, that works out to between 0.21 and 0.23 cm/pixel.
The chick looks to be slightly behind the egg and the character slightly in front, so let's make it an even 0.20 cm/pixel.
This makes our chocobo egg 36 cm tall.
To get a sense of the weight, let's compare this to other bird eggs.
Ostrich eggs average 15 cm long and weigh 1.35 kg. We should expect the mass to be roughly proportional to the cube of its length, which works out to 0.4 g/cm^3.
Large chicken eggs weigh at least 56.7 g and are about 5 cm long (source: my kitchen), or 0.45 g/cm^3.
(As a quick math check, this is about half the density of water. But we've essentially doubled the volume of the egg by treating the length as the side of a cube instead of the diameter of a sphere. That makes eggs about as dense as water, which makes sense.)
This makes our chocobo egg weigh 20 kg.