Which inequality expresses that gravity is the weakest force? If gravity is the weakest force that acts on an object, we should be able to write something much (!) better than, but similar to 
a $r^2$ / M  > G
to express that influences or accelerations a are always larger than those of gravity (of an outside mass M at distance r). Of course, the expression is wrong as it stands, as the acceleration a can be zero, due to other forces. 
What would be a correct or a better inequality that shows that gravity is the weakest force acting on a body? (The answer may need general relativistic or quantum theoretical concepts.)
 A: check out this page on Planck units or this page on the gravitational coupling constant or this article from Frank Wilczek to see what exactly is meant by "gravity is the weakest force".
quoting Wilczek:

We see that the question [posed] is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in natural (Planck) units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)].

While it is true that the electrostatic repulsive force between two protons (alone in free space) greatly exceeds the gravitational attractive force between the same two protons, this says nothing about the relative strengths of the two fundamental forces without saying something about the specific charge and specific masses. From the point of view of Planck units, this is comparing apples to oranges, because mass and electric charge are incommensurable quantities. Rather, the disparity of magnitude of force is due to the fact that the charge on the protons is approximately the unit charge (the Planck charge) but the mass of the protons is far, far less than the unit mass (the Planck mass).  That is why gravity between the particles is so much weaker.
A: The statement that "the gravity is the weakest force acting on a body" is not very exact therefore doesn't have a definite mathematical proof. 
For example for a body falling down the air drag is much weaker than the gravity.
But when gravity is compared to some other fundamental forces in some simple settings it is the weakest force.
For example in an atom nucleus the strong nuclear force is much stronger than electrostatic forces and gravity doesn't even count.
Or when you have two electrons in a distance the gravity is much weaker than electrostatic force.
One may suggest that because the gravitational constant is less than Coulomb's constant but that really is irrelevant because they're depended on the magnitude of other units within their respective formulas. If in Coulomb's law the unit of charge was nC the Coulomb's constant would be much less.
