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the effect is specific to jpg compression. quoting from here:

1. The representation of the colors in the image is converted to Y′CBCR, consisting of one luma component (Y'), representing brightness, and two chroma components, (CB and CR), representing color. This step is sometimes skipped.
2. The resolution of the chroma data is reduced, usually by a factor of 2 or 3. This reflects the fact that the eye is less sensitive to fine color details than to fine brightness details.

so, the contribution from Y takes the main chunk in the compressed image (it's almost the same as the grayscale)

(and btw, png encoding will have same (expected) compresssion ratio for bgr and gray)