It does take about 2-3 months before you see the full size of their eggs for the first season. Their second season they will usually lay less but bigger eggs.
They need to slowly stretch out to lay bigger eggs or else they will have troubles laying them.
Leghorns are used in large scale production because they have a good feed conversion and are highly productive. They were bred solely for egg production, where dual purpose breeds like australorps and rocks were bred for both egg production as well as having some meat qualities. Ironically they aren't very good at either one, and you are better off with straight egg producers if you want eggs, and meat breeds for meat. Dual purpose breeds do have value in that they are often friendly easy going birds and many will go broody.
So your leghorn will lay more eggs, eat less feed, but not really have much meat value. Her eggs will eventually be the largest, especially based on weight comparison of your hens.