Gravity is not, in fact, the attraction of lesser mass to greater mass. Gravity is the repulsion of lesser mass by greater mass.

In the case of the Earth, this means you are repulsed toward the Earth by the weight of the column of space "above" you, and are only prevented from falling through the Earth by its density. The Earth is relatively equally displaced by the column surrounding it, meaning you do not notice this effect.

Gravity seems to come in waves because all things in the relevant column are moving, but the shifting of mass is almost unimportant to your perception because it is such a small value. The magnitude and frequency is such that it goes unnoticed to all but the most sensitive equipment.

.... completely no evidence available, but, it sounds kind of reasonable.