Force 

A force is a push or pull upon an object's interaction with another object. Whenever there is an interaction between two objects, there is force upon each object. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of interaction.     

The gravitational force is a force that attracts any two objects with mass. We call the gravity force attractive because it always tries to pull masses together, it never pushes them apart. In fact, every object including you, is pulling on every other object in the entire universe!

Newton's universal law of gravitation 

The above definition of Gravitation force is also known as Newton's Universal Law of Gravitation. But if you go by the book then it is stated that "every object in this universe attracts each other with a force called gravitation which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres."   

Now to verify Newton's law of gravitation: Suppose that a body of mass m1 attracts another body of mass m2 with a force F towards its centre O1. The body of the mass m2 in turn attracts the body of mass m1 with the same force F towards its centre O2. Suppose the distance between their centres is 'd' then according to Newton's law of gravitation we have: 

        F ∝ m1 * m2                       (I) [keeping the distance constant] 

And F ∝ 1/d2                            (II) [keeping the masses constant] 

Combining equations (I) and (II), we have, 

F ∝ m1 * m2 /d2 

Or, F= G *(m1 * m2 /d2)                    (III) 

Where G is a constant of proportionality which is known as universal gravitational constant. The value of G in S.I. unit is 6.67*10-11 Nm2 Kg-2. Hence, the equation (III) gives the measure of the gravitational force between two bodies. This G can also be defines as the force of gravitation produced between two bodies of each unit mass each, separated by unit distance their centres. To furthermore prove the bold statement here is the equation and it's solution:

We have, 

F= G *(m1 * m2 /d2)

If m1= m2= 1 kg and d=1m. Put the value of  m1, m2 and d in the given relation,

F= G 1*1/(1)² 

Therefore    F= G

Relation of gravitation with it's factors 

1. The gravitational force between two bodies is directly proportional to the product of their masses.

2. The gravitational force between two bodies is inversely proportional to the square of the distance between them from their centres.

Gravity

Every object that has mass exerts a gravitational pull or force on every other mass. The strength of this pull depends on the masses of objects at play. Gravity is what keeps planets in  orbit around the sun and the moon around the earth. Hence, Gravity is a force that attracts a body towards the centre of the earth or any other heavenly bodies. https://www.britannica.com/video/179998/Overview-gravity-focus

So, in the difference there is a term called acceleration due to gravity which simply means acceleration produced in a freely falling body due to force of the gravity of earth. It is denoted by g and it's S.I. unit is m/sec² . Its average value is 9.8m/s² .

Mass & Weight

The amount of matter contained in a body is called mass of that body. Its unit is kg in the S.I. system. The weight of a body is defined as the force with which it is attracted towards the centre of the planet. Its unit is newton (N) in the S.I. system.

Free Fall & Weightlessness

When a body is falling freely towards the centre of the earth under the influence of the gravitational pull of the earth only, the motion of the body is called free fall. Weightlessness is the complete or near complete absence of the sensation of weight. This is also termed zero-G, although more correct form would be "zero-G force".



Some important points to remember:

• The value of g at the poles is maximum, hence weight is more there.


• The value of g at the equator is minimum, hence weight is less there.


• The value of g decreases with the increase in altitude, hence weight also decreases with the increment of altitude.


• The value of g decreases with the increase in depth, hence the weight also decreases with the increment of depth.


• 
  The value of g at the centre of the earth is zero, hence the weight is also zero.