When the plane moves, its going to move with the turbulence, right? Hence why the spirit level moves the minutist bit. However, if the earth was flat then the bubble would move to the far end when the pilot dips to account for the earths curvature. But it doesn't, because no dip occurs. Once again, if the earth was round and the pilot didn't account for the curvature, the plane would fly in a straight line and out of the sky into space, but this doesn't happen, therefore proving earth is not a globe.
Sorry to disappoint you, airplane leans on air and keeps altitude by air lift on wings.
Higher it goes the air is thinner and the lift on wings is weaker at the same speed.
That is why airplane needs maneuvering action to increase altitude.
If it goes lower, the air is denser and lift on wings is stronger, pushing it up.
That is how airplane keeps the altitude.
Not by straight line, but by balance in air density (pressure).
And that is why design itself doesn't allow airplane to fly off into Space.
The layer with constant density is not flat, it follows the Earth's surface.
Altimeter works like barometer, with scale calibrated directly in altitudes.
So, altimeter follows the layer with constant air pressure, not the flat line.
Another instrument used for decades in airplanes is Artificial Horizon.
It follows vertical lines, and vertical lines tilt with distances.
Two verticals apart from each other are both pointing towards the center of Earth, so they are not parallel.
Two verticals 1852 meters apart are tilting from each other for one arc minute.
That was why the nautical mile was defined to be 1852 meters in the first place.
It was defined to make navigator's job easier.
One degree is exactly 60 nautical miles (69 statute miles, 111.12 km).
If, for example, navigator measures travelled distance of 3 degrees 12 minutes, it will be 3*60+12 = 192 nautical miles away from, say, port they left.
As airplane travels, "down" is along new, current vertical, not along old vertical at "x" miles back.
Spirit level will follow the tilt as well, because weight of the liquid inside will pull towards new "down".
As airplane travels, artificial horizon self-corrects to new verticals as well, and pilot doesn't calculate "dip".
He just has to fly perpendicular to current vertical, which is along new horizontal, not the old one.
This is how artificial horizon self-corrects, and it is faster than the speed at which the airplane reaches new verticals.