If the earth stopped rotating, would we really fly inertially at 1000mph?
You would be sliding, because the friction between you and Earth would be too weak, or else you wouldn't survive the acceleration, if the rotation of Earth would be changed abruptly. That's like crashing into a wall with several hundred mph. This is with the exception of close to the poles.

Your weight wouldn't change much. On a smooth, plane, and horizontal surface you would slide (due to your inertia). Your velocity you would be sliding depends on your geographic latitude. At the equator it would be at the maximum. At the poles it would be zero. More precisely the velocity would be proportional to the cosine of the latitude (latitude 0 at the equator, and (+/-) 90 degrees, resp. $\pi/2$ at the poles).

Even more precisely, the speed you would be sliding would be $$2\cdot 465.1~ m/s \cdot cos ~\varphi,$$ with $\varphi$ the latitude.
Factor two, because superman accelerates to the opposite direction. Earth's equatorial rotation velocity is $465.1~m/s$.