For gravity does vary across the earth, meaning Newton’s apple has a slightly different weight in various other parts of the world and falls at slightly different speeds. That’s due to a combination of four factors.
First, there’s a latitudinal effect. The earth is not perfectly round: It’s flatter nearer to (and flattest at) the poles and bulges more towards (and most along) the equator.
Secondly, there’s a rotational effect. That difference in gravity between the poles and the equator is only partly due to gravity itself; it’s also caused by the fact that the earth spins faster at the equator.
Then there’s an altitudinal effect. Earth’s gravitational pull depends on your distance from its center. Gravity diminishes with altitude—but again, with fairly limited effect. If you’re 16,400 feet (5 km) up a mountain, you weigh 99.84% of what the scales would say at sea level.
Fourth differentiator: the tidal pull of the moon and sun. Although this has visible, repetitive and significant effects—the ebb and flow of sea levels—the variations this causes in the earth’s gravity are very small indeed.
While the first four factors can be compensated for mathematically, it’s the local geology which produces random gravity anomalies of the kind mapped here.
Newton's Apples (and Your) weight is more in Illinois than in Indiana