It's having a very tiny effect on the length of a day. From time to time, the International Earth Rotation and Reference Systems Service needs to insert a leap second so that atomic clocks match the real day, and tidal drag is the main reason for it.
But none of this has ANY effect whatsoever on gravity on Earth. The ONLY thing that affects that is the mass of the Earth. That's going up slightly all the time because we collect space dust and meteorites, but that's a TINY amount compared with the actual mass of the Earth. It's like a tiny sprinkling of dust you would hardly notice. And all that would be the same if the Moon wasn't there at all.
In any case, the Moon's orbit isn't exactly circular. It's slightly oval, as is our orbit round the Sun. So it's closer at some times than others, and if that had any effect on gravity, you'd notice a difference in your weight when you weigh yourself at different times of the month. And you don't, do you?
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az_lender say: The moon is moving away from the earth at more like 4 cm every year. That has absolutely no effect on the earth's gravitation, though in the long run it will make our ocean tides less prominent than they are now. Don't care how "adamant" he was -- he is IGNORANT!!!
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Sciencenut say: The Moon is receding from Earth, by maybe 1 cm/year. Gravity does not change, but the Moon is going into a slightly higher orbit. This is because of tidal friction of our oceans against our continents, which gradually slows down Earth's rotation, and transfers this rotational energy to the Moon, which then puts the Moon into a slightly higher orbit.
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INBREAD CHRISTIAN say: No, neither of you are that smart.
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brad say: Gravity is an effect of matter, so gravity DOES change on earth every year. The earth grows in mass by about 2000 tonnes per year (from space dust) so our gravity is increasing. Only by the tiniest fraction, though.