Using a proton charge 1.602*10^-19 coulombs is equal to proton mass 1.673*10^-27 Kg.
One coulomb = 1.673*10^-27 Kg divide by 1.602*10^-19
Therefore One coulomb is equal to 1.044*10^-8Kg.
Therefore One coulomb is approximately equal to a plank mass.
Knowing that the gravitation constant G used for calculating a plank mass relies on acceleration due to gravity g measured in a given location, the two should be the same.
https://en.wikipedia.org/wiki/Planck_mass
https://en.wikipedia.org/wiki/Gravitational_metric_system
The ratio of proton mass to Planck mass is dimensionless, while the proton charge measured in Coulombs depends on this completely arbitrary unit. Hence, the coincidence is completely arbitrary. There is a natural dimensionless expression for the proton charge, in which it is approximately 0.3 --- quite a few orders of magnitude off.
According to the Standard Model the scale of hadronic masses is determined by Lambda_QCD, the scale where the running strong coupling "constant" becomes large.
The measurement of the Newton constant of gravity G does not depend on the acceleration of gravity (which would require an independent measurement of the mass of the earth). To learn how it is done, search the web for f.i. the Cavendish experiment. It appears that the principle of this experiment from 1798 (inspired by Coulombs measurements of electric forces by the same principle) is still being used.
In fact the ``proton charge'' (the electric charge of the proton) is the coupling constant of the proton to the electromagnetic field and (a) is dimensionless in four spacetime dimensions and (b) its value depends on the energy/length scale it's measured at-standard renormalization group flow.
The statement of the question is, in fact, meaningless, since the charge-to-mass ratio of the proton doesn't have the same dimensions as a mass, so a comparison of their numerical values doesn't make sense in any case.
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