It was Galileo who first seriously suggested we remove the distinction created by Aristotle between two realms with distinctly different physics.
In "... The Two Chief World Systems ...", he introduces the notion of the inertial frame of reference, as experienced on a boat, as the normal compromise between the stationary and the moving, and suggests reasoning about the heavens as large moving objects more like boats, and less in an idealized a priori way.
Newton had already a century or so of other thinkers inspired by Galileo before he proposed a single unifying law in a mathematical form that would explain both equally well. This included Kepler, who solved the primary problem Galileo's astronomy introduced -- that circular orbits do not capture most of the subtleties of planetary motion, but elliptical ones do.
Newton has to have been moved by the quadratic nature of Kepler's astronomical geometry, and Galileo's knowledge that gravity on earth was quadratic. (The rule is captured in the book in terms of Fibonacci numbers, but that breaks down straight into squares.) So our tendency to think this was just single act of genius and not an integration of scientific details, is kind of overstated. In fact, if Hooke is not lying, both of them computed the same position of a comet based on Kepler, by fitting it to a conic section, before Newton's work was published.
In the text, Galileo does not seem to employ the principle of sufficient reason per se, but he relies strongly on the idea that needless variation, especially when it must be extreme, is an indication of a poor argument. For instance, if the stars move on the spheres, some spheres spin at different rates than others to achieve the apparently consistent motion of the skies on Earth, the farthest spheres must turn quite quickly, whereas if the Earth spins, then stars at all different distances from us just move at some fairly consistent speed.
(He also continually points out that Aristotle himself would not put up with the level of authority assigned by everyone to Aristotle himself. So he may have wanted to avoid dependency on other a priori notions in Aristotle on the modern side of his argument.)
Whitehead in "Science and the Modern World" seems to think that from Thales on, almost everyone presumed that physical laws were uniform throughout the universe. He thinks that this notion of trustworthy uniformity is somewhat characteristic of the West, reflected in Greek drama and Roman Law, and is a sort of shared para-religious impulse behind the nature of our science.
That makes Plato's and Aristotle's notion of two separate realms kind of an aberration, that was eventually ironed out.