An "experiment"?.... i am not denying the value of g on earth is not 9.81, but the reason why it is 9.81
Not only can it be done by observation (experiment) but by using newtons law of gravitation which assumes the world is round.

, what part did you not get?
i droped an object and measured how long it will take to hit the ground, then i repeated the process from a higher altitude, and then again, from the higher altitude, i used a stopping mechanism, and a clock with accuracy down to the fourth decimal spot. I observed the results, and with some calculus, came to the conclusion that the earth accelerated toward the object i dropped, with an acceleration of 9.82 m/s^2 .