(Btd) The moon, full or otherwise, always looks big when close to the horizon. It's an optical illusion, which nobody can really explain. If you actually measured it you would find it's smaller near the horizon than when high in the sky, other things being equal. This is a simple geometrical effect.
[Rosie] No, I think, surely, you would find that the Moon is the same size in the sky no matter whether it's high or low. After all, it only takes a few hours for it to rise or set - it's not going to change in apparent size as it does so. The apparent growth of the Moon when near the horizon is of course some kind of psychological effect.
The reason the Moon has been looking even bigger than usual near the horizon this week is that full moon has coincided (almost) with midsummer. The Moon is full when it is opposite the sun in the sky. The sun is at its highest at midsummer. Therefore, if the Moon is full at midsummer, it will be as close to the horizon as it ever gets whilst being full. Therefore the "Mendex" or Moon Illusion is at its strongest.
When I say that the Moon doesn't change in apparent size while rising or setting, I mean that the area of sky that it covers surely doesn't change. Obviously its apparent size does change because it looks bigger closer to the horizon, but it extends over the same arc of the sky (and indeed of the retina).
The moon should appear to be smaller when on the horizon than when at the zenith. Reason? It is further away when viewed at a tangent to the Earth's surface than from a perpendicular. This slight change is measurable though unlikely to be noticed by a casual observer. Why we generally perceive a full moon to be larger on its rising as opposed to when it is high in the sky has often been said to be as a result of it being in proximity to our more normally observed everyday horizon (trees, buildings, horizon line) than when it's clear of such. In other words the sense of scale becomes more evident.