It moves a very little. It moves so very little that it isn’t measurable because even if you are unbelievably morbidly obese your mass is insignificant compared to that of the Earth.
Let’s say you weigh a health 100kg. The Earth has 60,000,000,000,000,000,000,000 times your mass.
Obligatory [XKCD](https://what-if.xkcd.com/8/) reference.
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