The moon looks bigger due to a well know illusion, essentially when it's low in the sky we can compare it with objects in the line of sight, this makes it look bigger. The apparent size of the moon varies with distance but it's almost imperceptible.
The Moon has an elliptical monthly orbit around the Earth. The Moon is closest when apogee coincides with a Full Moon (especially in winter when the Sun is also closer) because it is aligned with the Suns gravity. This calendar shows the distance to the Moon at apogee (closest) and perigee (furthest) points in its orbit.