What are the physical laws for upscaling an RC model to 1:1?
This is not a full answer: much is mentioned by Michel Touw, but I'd like to correct a common misconception.

The mass growing as the third power of linear dimensions applies only to solid objects. But the airplane is not solid; rather, it's a thin-skinned frame. (Unless it's a solid foam RC model). Therefore, its mass should grow with the area, as the square of length.

However, this is, of course, not quite true. In reality, you need thicker skin, thicker spars, etc., and these elements will get heavier 'properly' with the cube of length - and even more, because they'll need to support themselves as well, with their added mass.

In the end, the mass of airplanes grows between the second and third power, and much closer to second.

Let's take B734 and B772 for example, which differ close to twice in linear size. Their empty weight (roughly 33 and 140 tons, depending on modification) differs by 4.25 times, which is approx. 22.1. MTOW has a similar ratio: 68 vs 300 tons, 22.15.