Solution

1. Free Fall:
We feel heavy because we are pushed against the Earth, a chair, a bed etc. all the time (and they "push" against us with the same force) whereas in free fall we push against nothing (and nothing pushes against us) and therefore we do not feel heavy.

2. Center of the Earth:
If the counteracting attractional forces which act on us compensated each other, we would not feel the gravitational force. The astronaut could therefore float weightlessly in the center of the Earth, if he could stay there.