I don't have that much experience with this, but I'll share what happened with me. I've got a mixed hen from when one of my girls went broody last year. She's Golden-Laced Wyandotte (cock) x Red Star (hen) mix, and her eggs are just as big as a Red Star's but a little lighter in color from the Wyandotte side. She's something of a throwback to the genetics from her mom's side though, she's white and red. I had a beautiful red and black pullet from the same cross and a hawk killed her right before she would have begun laying.
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I'd really like to know the answer too! Selecting large eggs is sensible, but large eggs is ALL down to the female. A hen will lay roughly the same size of eggs whether or not they are fertilised and no matter who fertilises them. But egg size might be inherited from the male side... I remember reading ages ago that egg laying ability (numbers) is inherited from the male, so your daddy roo should be chosen for his mother's laying ability. If you mate your most productive hen to a roo whose mother was a rubbish layer, any resulting pullets will also be poor layers. I can't remember where I read this though...