In very rough terms, the earth and moon can be considered an object with a centre of mass somewhere between the centre of the earth and the moon.
This centre of mass will be near the earths core due to the relative sizes of the bodies.
This centre of mass will also be mobile as the moon revolves around the earth.
Thus, a person standing on the earths surface will be moving in and out relative to the centre of mass of the earth/moon pair and will experience (very tiny! 2micro m/s2) variations in gravity.
They would also be moving in and out relative to the L1 Lagrange point, ie varying their range from a point of zero g