IIRC, it's surprisingly not well understood why inertial mass equals gravitational mass, at least to high observational precision (which isn't all that high in the grand scheme of physicsthings, because gravity is difficult to measure).
The reason given by General Relativity, is that space itself is moving, accelerating towards gravitational wells. There was an excellent animation of this in a recent YT video, which of course I didn't bookmark, so if someone can remember it please put it here -- in any case, the fact that spacetime itself is curving in towards a mass, is equivalent and indistinguishable to inertial mass being accelerated.
What's
weird about the picture is not that space is accelerating, but why we
aren't when we stand on the Earth! Well, the answer is relative, of course -- since space is moving past us here on the surface at ~9.8 m/s^2, something must be accelerating us up through all of it. The force for that eternal acceleration is -- drumroll -- the force of your weight pushing you along, and so on down to the core of the Earth where all the force, from the entire mass of the planet, is bearing against itself; fortunately, planetary matter is not very compressible at these pressures (but it isn't resistant to shear, and so the Earth gets pulled into a sphere, more or less -- it reaches hydrostatic equilibrium).
So, obviously that weight exactly equals your inertial weight, because otherwise you'd be dragged along in space at 9.8 m/s^2 relative to the Earth's surface.
There are some weird ideas, like Mach effects, which I don't think have been disproven? Or perhaps they're equivalent after all, but we don't quite yet understand how. The deeper mystery is how to integrate General Relativity into the Standard Model, so that we have a complete understanding from the smallest quantum level to the scale of the entire universe. Perhaps then we will have a more complete explanation. That, however, will take some time it seems.
Also:
Purely from Newtonian mechanics, there is no answer, of course. Newton's laws can be derived from Relativity given suitable approximations (c --> infty), just as Relativity is an approximation of some as-yet-unknown better model, and so on (it's turtles all the way down, at least until we have a more convincing reason to believe otherwise).
Tim