We'll start w/ a regular cube, and a daz 3d woman. To make things simpler we'll be growing. The same principles work in reverse for shrinking.
Now we'll double the height. Just the height. This is scaling on the line.
Okay, see how tall and thin she is. And notice that there are two boxes, so the weight has been doubled. To make her look more like a person and less like a Na'vi we have to double the width, too. This is scaling on the square.
She's actually sort of squashed flat So we have to double the breadth as well. We have to scale on the cube.
My height is one/tenth normal. On the line. My surface area, shoe size, and some other things is one one-hundredth normal, or on the square. My weight is on the cube. One one-thousandth what it had been the night before.
More information can be found at Square-cube law on Wikipedia and Square Cube Law on TVTropes, The Biology of B-Movie Monsters, and On Being the Right Size by J. B. S. Haldane.
You can also look at The Physics of Superheroes: Spectacular Second Edition by James Kakalios and Insultingly Stupid Movie Physics: Hollywood's Best Mistakes, Goofs and Flat-Out Destructions of the Basic Laws of the Universe by Tom Roger.
Yeah, it's messed up, and I'm still not used to it.