In the 1960s, NASA sent a set of probes to orbit our moon called the Lunar Orbiter Project. The idea was to take pictures for possible Apollo landing sites. While monitoring the probes, NASA scientists noticed they would sometimes speed up and dip towards the moon while in orbit. After investigating, the realized it was due to localized changes in the moon’s gravitational field.
And it’s not just the moon. The experience of gravity on any planet can depend on its density and what type of matter is underneath the spot being measured. On a planet like Earth, other things can affect it too, like the tides, how much mantel is below the crust, and even where the moon is at the moment. This means though your mass stays constant everywhere on Earth, your weight can change.