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Take a ball. take it on top of a tall building. Drop it with zero velocity downwards.  Measure its position at each second and fraction of second.

Find the speed and acceleration of the ball at each time t and height h.   Multiply the mass and acceleration to get a value of force.

Let the ball fall into a sand heap. Note the depth of the dip it makes.  That dip indicates the force with which the ball is attracted by the EArth.  Take a bigger ball and do the same.  Note the dip in the sand heap.  It will be deeper.

You will find that the dip in the sand is directly proportional to the mass of the ball.  So we can find that gravitational force is proportional to mass of the object.

We can probably do the experiment that Scientist Cavendish did to measure the gravitational force and find the value of G, gravitational constant.

Two small balls of equal mass are attached to two ends of a long light rod forming a dum b-bell.  It is suspended at the center by a thin quartz wire.  There are two more spheres arranged at the same horizontal level and at the end of a diameter, whose length is same as the length of the rod we have taken.

The dum b-bell is brought near the two balls.  Then all the four balls are on the same horizontal circle.  Now attach a small reflecting mirror to the quartz thread.  Focus a light ray on to the mirror. 

Due to the gravitational attraction between the balls, the light ray is deflected when the dum_b-bell moves closer to the other balls.  The deflection is due to the torsion developed in the string due to gravity force couple.
Measure the deflections.  In this experiment,  we can repeat it with different masses of the balls and we can place the balls at different distances, then we can find that the deflection (torsional).  It will be proportional to the masses and inversely to the square of distance.

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There is a popular story that Newton was sitting under an apple tree, an apple fell on his head, and he suddenly thought of the Universal Law of Gravitation. As in all such legends, this is almost certainly not true in its details, but the story contains elements of what actually happened.  according to me this can b your answer