My birds are all pullets still with the oldest at 6 months so size I can't really address from experience. My roosters are big but they don't get in the nests.
From what I have read it won't bother them. All these nests, it seems that folks that put out a straw filled tray have fine success. They sell for about $22 here. Next year I will let you know if any of my fat hens like them. 

