Luna2uno, I still don't understand your question. I'm pretty confused about what you're asking right now. I've only skimmed the last half of the thread, but let me attempt a response.

As papageno said, don't confuse mass and weight. Mass is an intrinsic property to matter, where as weight is force caused by gravity and determined by mass, distance, and the value of G. (The equivalence principle does not apply here, as a = G*M/R^2 [your mass, m, remains the same].) The amount of mass here where G=G would be the same amount where G'=2G.

Now, different systems of units are a completely different beast. Your story seems to discuss different systems of units. The amount of mass is the amount of mass is the amount of mass, no matter how it is defined. A mass of 10 kg is the same amount of mass whether measured in kg, g, slugs, or whatever. 10 miles is the same distance if measured in miles, feet, meters, or parsecs, in just the same way as above. It's also true that G has different numerical values in units of kg,m,s, or g,cm,s, or slugs,feet,fortnights, but these are all the same value.

Mass doesn't change if G does.