Chickens give larger, more valuable eggs the more they like you. You can improve the relationship by picking them up (and putting them down again) once per day, letting them out when it is sunny, keeping them inside when it is raining or snowing, and feeding them Chicken Feed by hand (instead of using a feeding tray). Giving treats helps boost relationship too.
It is important to note that relationships are per person. If playing in multiplayer, if you want large eggs you will have to personally raise your relationship with the chickens.