Well, there's the answer that it's what seems to fit the facts. GR may be one of the primo-grade "unreasonable effectiveness of mathematics" examples as it captures rather complex (to human minds) behavior in a handful of carefully-defined symbols, but technically it's still an empirical theory first and mathematical theory second.
Secondly, as others mention, there is the obvious answer that r^2 is how area changes as you increase the radius of a hypersphere in 3-D space; here I deliberately say "hypersphere" even though we're in 3-space here just to emphasize that it's particular to the the 3-D case. There is a theory that the reason gravity is so much weaker than the other forces is that it is "escaping" out in other dimensions we can't see, though that still leaves the stuff we can see expanding as inverse-square in what we can see.
(One of my favorite crazy dark-matter theories is that it lies in those other dimensions, and the reason we can't capture any is that it is literally not "in our dimension". That said, it still can't be conventional baryonic matter, because dark matter doesn't clump anything like it does. If there was a "parallel universe" or 10 just like ours, except they gravitationally interact, we'd see things like stars in orbit around "nothing", because the stars in the parallel universes are interacting. That's not what the universe looks like.)
Well, there's the answer that it's what seems to fit the facts. GR may be one of the primo-grade "unreasonable effectiveness of mathematics" examples as it captures rather complex (to human minds) behavior in a handful of carefully-defined symbols, but technically it's still an empirical theory first and mathematical theory second.
Secondly, as others mention, there is the obvious answer that r^2 is how area changes as you increase the radius of a hypersphere in 3-D space; here I deliberately say "hypersphere" even though we're in 3-space here just to emphasize that it's particular to the the 3-D case. There is a theory that the reason gravity is so much weaker than the other forces is that it is "escaping" out in other dimensions we can't see, though that still leaves the stuff we can see expanding as inverse-square in what we can see.
(One of my favorite crazy dark-matter theories is that it lies in those other dimensions, and the reason we can't capture any is that it is literally not "in our dimension". That said, it still can't be conventional baryonic matter, because dark matter doesn't clump anything like it does. If there was a "parallel universe" or 10 just like ours, except they gravitationally interact, we'd see things like stars in orbit around "nothing", because the stars in the parallel universes are interacting. That's not what the universe looks like.)