Yeah, it's the refractive index, which varies, in turn presumably due to the variations in density due to hot air being lighter.
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Yes. The moon pulls on you slightly more than the center of the Earth because you are a bit closer than the center is. So you're lighter. And also, 12 hours later, when the Moon is the other side of the Earth from you, you're slightly lighter as well, because the center of the Earth is accelerated towards the moon slightly more than you, it turns out that this makes you slightly lighter as well, by the same amount.
Due to gravitational effects, you weigh slightly less when the moon is directly overhead