First of all, I have to say I'm neither a astronomer nor a professional professor. I'm just super creative I'm a designer.
I believe the moon looks bigger at horizon not only because of the moon illusion, shape constancy and size constancy, etc... But also the gravity.
One theory about the moon illusion says that when the moon is near the horizon we perceive it to be farther away from us than when it is high in the sky. But since the moon is actually the same size, our minds make it look bigger when it is near the horizon to compensate for the increased distance.
While upon this theory, its the gravity which tricked us to see the bigger boon at horizon. I don't want to explain since I don't think I can explain well, feel free take the idea and make ur own explanation.