Consider a positive integer. Should it have more prime factors or less? Should you assign more weight or less weight to a positive integer that has more prime factors? Answer: No, it should have however many prime factors it has, and the weight you should assign depends upon your purpose.
Entropy gives you an idea of how "predictable" the image is. An image that is all the same is entirely predictable and has low entropy. An image that changes from pixel to pixel might at first thought be unpredictable, but the change might follow a pattern, such as a "checkerboard pattern", so changing every pixel does not mean that it is difficult to predict. Compression algorithms try to discover predictability. Each aspect of predictability requires some storage to represent, and the more storage that an image requires to represent its predictability then the higher the entropy the image has. Suppose you had the ultimate most efficient general purpose compression algorithm, then entropy would correspond to the smallest file size that was needed to represent the image. (There is a formal definition related to this, Komogorov Complexity)
But this does not answer the question of how much weight you "should" give an image, because you have not indicated what purposes you are trying to achieve.
Approximately speaking, an image with higher entropy is "more specific", more detailed. If your purpose were, for example, to decide that the image represented "a feline" then high entropy is not needed, but if you are trying to decide whether you have correctly identified an individual lion, then you want a fair bit of detail in the picture, probably more entropy.
