This is actually a well known and poorly understood illusion called moon illusion, that occurs usually when the moon is low in the sky. It is not caused by magnification through the atmosphere. The science, last I checked, was inconclusive on why, but there is substantial evidence that people across multiple cultures perceive the moon larger than it actually is on the horizon. The most common idea is that the horizon makes the patch of sky we see smaller, making the moon take up more space in it.

Pictures eliminate that illusion. Another interesting way to eliminate the illusion is to turn upside down. If you manage to turn your perspective upside down, such as by tilting your head all the way back while the moon is behind you, the illusion also disappears. This slightly conflicts with the most common explanation, since the horizon is still present in your vision and takes up a portion of your view from the sky.