Built on

P. D. Mannheim and D. Kazanas, “Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation,” Gen. Rel. Grav. 26
1994
Earlier work this paper cites.
G. T. Gillies, “The Newtonian gravitational constant: recent measurements and related studies,” Rept. Prog. Phys. 60
1997
Earlier work this paper cites.

Similar

E. Anderson, J. Barbour, B. Foster and N. O’Murchadha, “Scale invariant gravity: Geometrodynamics,” Class. Quant. Grav. 20
Original
2003
Cited alongside, same era.
P. D. Mannheim, “Alternatives to dark matter and dark energy,” Prog. Part. Nucl. Phys. 56
2006
Cited alongside, same era.

Then

P. D. Mannheim, “Making the Case for Conformal Gravity,” Found. Phys. 42
Original
2012
Later among the works it cites.

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2013

Problems with Mannheim's conformal gravity program

Yoon, Youngsub

Understand

We show that Mannheim's conformal gravity program, whose potential has a term proportional to $1/r$ and another term proportional to $r$, does not reduce to Newtonian gravity at short distances, unless one assumes undesirable singularities of the mass density of the proton.

Therefore, despite the claim that it successfully explains galaxy rotation curves, unless one assumes the singularities, it seems to be falsified by numerous Cavendish-type experiments performed at laboratories on Earth whose work have not found any deviations from Newton's theory.
Moreover, it can be shown that as long as the total mass of the proton is positive, Mannheim's conformal gravity program leads to negative linear potential, which is problematic from the point of view of fitting galaxy rotation curves, which necessarily requires positive linear potential.