1) The 300 miles is above the surface of the earth, not from the center of the earth. If the astronaut is 300 miles above the earth and the radius of the earth is 3960 miles, the astronaut is 3960+ 300= 4260 miles from the center of the earth.
2) Your formula has but you didn't square!
3) Since weight is inversely proportional to the distance, you should have
But that is NOT the 1.54 pounds. 300 miles is relatively small compared to 3960 so you really haven't gone a great distance, comparatively. And how is the astronauts weight to be measured? Is there more to the problem you haven't told us?