The Planck time is NOT infinitesimal. Infinitesimal is defined as 'smaller than any Real number'. The Planck time is not smaller than any Real number, because its a Real number. And the Planck mass is small by human scales but on particle physics scales its staggeringly enormous. Using a set of scales to weigh out a mole of substance does use G, but it doesn't have to. Mass is not defined by weight but its inertia. 12g of Carbon can be measured out in a weightless environment. It's just convenient to use weight when you're on the Earth's surface doing practical things. The Planck mass has nothing to do with N_A, you need absolutely zero knowledge of N_A to work with the Planck mass. Yet again, you stumble through a bunch of concepts obviously a little too advanced for you.