Question

Why is acceleration negative in a free fall?

Answer 1

Whether acceleration is positive or negative is entirely a result of your choice of coordinate systems. If you define the ground as position zero and points above that to have positive altitudes, then the acceleration caused by gravity points in the negative direction.

It is interesting to note that when you are standing, the floor beneath you exerts a force resisting your free fall. This force is up (in the positive direction) keeping you from falling into the center of the earth. Gravity still acts in the downward direction. And the upward force from the floor is equal and opposite to your weight.
Weight is mass times the force of gravity.
`weight = mg`