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But what's the integral of 1/r^2 from 0 to \infty ...that's the part not that not squaring up.

Newtonian gravitational potential of a point mass at origin of mass M is - GM/r so at r = \infty the potential is zero. Well, partly just by definition.

I believe we are assuming different models and I want to understand yours.

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Because everything in the real universe occupies a volume, and therefore no two distinct "things" can be 0 distance apart. The distance between two marbles' center of masses is the sum of their radii. So if you want to measure the potential gravitational energy between the two marbles, you'd take the integral of (GM^2/x^2) dx between x = [sum of radii of marbles] and x = infinity, as an approximation.

Ah! I was talking about the abstraction of point masses, then there is the shell theorem. But now at least I understand the discrepancy.

In any case gravitational potential at infinity is formally defined as 0 in Newtonian physics.

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