Thank you for clarifying!
When I converted with Calibre Kindle didn't see included fonts - there was no option for publisher font so mobi looked different (worse) than epub.
But now I see I missed additional settings for output file and I had "old" mobi set.

I converted to "both" and now not only fonts are fine, but the file is the same size as epub and not twice as big like it was after conversion with previewer.
Thank you!