The problem is that when working in scale not all the physical characteristics do scale in the same way. It's a common problem when making tests on scale models for research or design purposes.

But if we talk about size, your evaluation of the weight going with the square of the linear dimensions is right, since weight is proportional to volume x mass density, and the latter can be assumed as a constant value in our case.

But the base assumption is that you cannot have a full scale model, meaning you cannot have a 1/16 size model, with scale weight, scale power, scale speed and accelleration, scale air drag and ground friction, etc., at the same time.
Weight, size, speed and accelleration can be obtained at the same time, however.