Your formula is wrong. It's either:

    F_{a} = F_{b} = G * m_a * m_b/r^2

    \vec{F} = G * m_a * m_b/|r|^3 * {\vec{r}}

You find that by studying physics, not history of physics.

> it would have been intellectually pleasing(at least for me) to know how Physicists came with it, what's the motivation behind 1/d(A,B)^3, how did people come up with G, how it was measured, etc.

Yes, understanding a specific change in the state of physics at time T is most certainly helped by understanding it at time T-1. But make no mistake here, this is still physics and not history of physics (whatever that means).

Conceptually the least action principle is the fundamental concept in classical mechanics, everything is derived from it, plus symmetry.

Historically this has all been done backwards. Once you have Newton's law of universal gravitation, it's trivial to prove that the gravitational flux must be constant for every enclosing surface. It's easy, in terms of mathematics required, to come up with a least action principle from that (albeit not as easy as the inverse deduction). However, if you think of Newton's laws as fundamental, it is not a very natural thing to do. Why would you do it? Lagrange was a very deep thinker to see why the least action principle is the truly fundamental thing. He was doing this way before Noether's theorem. He was doing this before the concept of energy was formalized! They knew that a quantity with what we now know as units of energy was conserved, and they knew momentum was conserved, but they didn't know what these things were, especially as no other form of energy except kinetic and potential energy was known back then. Truly a visionary thinker.