Is there a way to resize an image without creating new colors in the output image?
A nearest-neighbor resize will do what you ask but I am not certain it will give you much smaller tiles.

It is quite likely that the tiles made from the original image are smaller simply because they have less high frequency content and thus compress far better.

You can look at it the other way around: there are more terrain features in the tiles of the resized image so it takes more space to store them. That's a very gross simplification of the truth, of course. And it assumes a reasonably efficient compression algorithm.