After reviewing the basics of Non-inertial relativity theory based on the existence of a maximal proper force $b$, it allowed to postulate a modified Newtonian attractive gravitational force (and potential) which is $finite$ at the origin : $ | F ( r = 0 ) | = b$, and which vanishes at $r = infty$. Secondly, from the modified gravitational potential energy we were able to glean the expression for a running gravitational coupling $ G ( r ) $ which exhibits asymptotic-freedom-like properties : $ G ( r = 0) = 0$, and $ G ( r = infty) = G_N$. No quantum corrections were necessary to decrease the strength of gravity at short distances. Thirdly, we found that for very $large$ masses $m_1, m_2$ (compared to $ sqrt b $) the $threshold$ in the values of $r$ obeying $ kappa r^2 < < 1$, where the non-Newtonian regime becomes manifest, becomes larger and larger as $m_1, m_2$ become larger and larger. Whereas for very $small$ masses (compared to $sqrt b $) the $threshold$ in the values of $r$ obeying $ kappa r^2 < < 1$, where the non-Newtonian regime becomes manifest, becomes smaller and smaller as $m_1, m_2$ become smaller and smaller. In the $ b = infty$ limit one recovers the Newtonian gravitational force for all values of $ r>0$. These results were all possible by abandoning the weak equivalence principle at short distances.