@panomies and @Chaotic_Sys already gave the theoretical file sizes for uncompressed 3-channel RGB image files saved at 16-bit integer precision. I have a Sony A7 camera, which saves 6000 by 4000 pixel raw files, which before interpolation are roughly 24Mib. A sample raw file exported as an uncompressed png from RT was 138MiB, and the compressed png was 105.3Mib. Opening the uncompressed png with GIMP-2.9 and saving it to disk using maximum compression produced a 105.3Mib file, same size as the RT-compressed png.
Uncompressed interpolated image file sizes as saved to disk by a raw processor are completely independent of the file size of the original raw file saved by the camera. The real mystery isn’t why RT pngs are so large, but why the Sony raw files are so small. As amply documented on the internet (https://www.dpreview.com/articles/2834066212/the-raw-and-the-cooked-pulling-apart-sony-raw-compression is a good place to start), Sony “lossy compresses” the raw files for A7 cameras and presumably does the same thing with your A6000. Looking at some numbers:
Nominally the A7 and I’m guessing also your A6000 are 14-bit cameras. So in theory the raw files should be roughly 40.1 megabytes in size:
4000px high times 6000px wide = 24000000 pixels
Times 14 bits per pixel = 336000000 bits
Divided by 8 bits per byte = 42000000 bytes
Divided by 1048576 bytes per megabyte = 40.1 megabytes, not counting exif data and any thumbnails.
In reality the Sony raw files are “lossy compressed” (information is permanently lost) using a two-stage compression algorithm. The first stage reduced the nominally 14-bit capture to 11 bits. If this were the only compression, then the resulting raw files should be roughly:
4000px high times 6000px wide = 24000000 pixels.
Times 11 bits per pixel = 33000000 bits.
Divided by 8 bits per byte = 1048576 bytes.
Divided by 1048576 bytes per megabyte = 31.5 megabytes.
Sony’s “second stage” compression takes the file size all the way down to 24 megabytes, which is slightly less than the amount of space it would take to store an uncompressed raw file saved by a 9-bit camera. Remember, this is lossy compression all the way, lossy compression to 11-bits of information per pixel, and then further lossy compression down to somewhat less than 9 bits of information per pixel.
Here is a nice link which explains the various “bits to bytes to megabytes” calculations: