It seems TGA and PSD are the fastest image format read by stb_image. TGA is an old uncompressed format with support transparency layers, uncompressed images have the same size on the disk and in memory. PSD is compressed with RLE which is really simple and fast to decode however it do not compress a lot the image. I think I will be using PSD for the most sprite sheets now.
For my sprite sheets generator, I have had some problems with CImg trying to generate a sprite sheet with a lot of small images. So I now use OpenCV for the generation which seems to be the standard for computer vision. OpenCV is quite heavy, but everything is reliable and really fast compared to CImg.
The last level progresses a little bit each day and becomes bigger and bigger. This level has a lot of big images, for example, the level objects and one map need three sprite sheets. So maybe I will split the objects along maps more to balance the loading time and improve memory footprint.