Why is gravity different from other forces? Unlike other forces, the "amount of force" gravity applies to different bodies is different. for example, if your hand has the force of 10 N, it could have accelerated a body with the mass of 1 kg to $10 \ m/s^2$, and a body with a mass of $2$ kg to $5 \ m/s^2$. Unlike that gravity "pulls" bodies with the same acceleration ($\approx 10\ m/s^2$), that means that it applies $10$ N to a body with a mass of $10$ kg, and $20$ N to a body with a mass of $2$ kg. Why is that?
(if you can simplify the answer that will be appreciated, I just learned Newton's laws of motion, so I probably won't understand advanced material).
 A: As others have already pointed out, the amount of force an electric field applies is also different for different bodies. So gravity is not unique in this respect.
What is unique about the gravitational field is that all masses experience the same acceleration in a gravitational field. If one doubles the mass, the acceleration remains the same for a given gravitational field. That is not the case for electric fields.
So why is the acceleration due to gravity a constant? It is because mass has a property called inertia, meaning it resists a change in motion (resists acceleration) per Newton's first law in proportion to the magnitude of the mass. If you double the mass, you double the resistance to acceleration, effectively requiring double the force to obtain the same acceleration.
The force $F$ on an electric charge $q$ for a given electric field $E$ depends only on the magnitude of the charge and has nothing to do with the mass of the charge.
$$F=qE$$
On other hand the acceleration $a$ of the charge depends on both its mass $m$ and its charge $q$ per Newtons second law
$$F=qE=ma$$
$$a=\frac{qE}{m}$$
Clearly an equal amount of positive charge $q$ (associated with protons) and negative charge $q$ (associated with electrons) will experience the same magnitude of force in the same electric field, $F=qE$, but different accelerations due to the mass of the positive charge being much greater than the mass of the same amount of negative charge.
Hope this helps.
A: There are other types of forces that have similar properties.  The best-known ones are electric and magnetic forces.  An object with 2 C of electric charge will feel double the force of an object with 1 C of charge, all other things being equal.
What is unique about the gravitational force is that the quantity which determines the amount of force an object experiences (the "gravitational mass") is the same, for all objects, as the mass that appears in Newton's Second Law (the "inertial mass".)  It didn't have to be this way;  for example, for charged objects, the electric charge is what determines the amount of force, but the same inertial mass determines how much acceleration this force creates.  But for gravity, the two quantities are exactly equal (so far as we can tell), and so every object ends up having the same gravitational acceleration regardless of its mass.  This remarkable coincidence is the basis of Einstein's equivalence principle, on which the theory of General Relativity is based.
A: 
Unlike other forces, the "amount of force" gravity applies to different bodies is different.

That isn’t actually a difference. An electric field gives a different force to different bodies also. Consider an electron, a proton, and a neutron in the same E field.

Unlike that gravity "pulls" bodies with the same acceleration (approx. 10 m/s^2), that means that it applies 10N to a body with a mass of 10kg, and 20N to a body with a mass of 2kg. Why is that?

That is because the force of gravity is proportional to mass. This is different from electromagnetism where the force is proportional to the electric charge. Note that the proportionality of the force of gravity to mass is quite important. It leads to the equivalence principle, the geometrization of gravity, and the treatment of gravitational force as an inertial force.
