Here some thoughts about your example :
01. There is a quality gain but it's imperceptible to the eye. You don't see it but the noise, sharp edges and others picture details are reproduced more accurately. That's why the file is bigger.
02. Never, never, never use bitrate as a quality measure, it's not. At the same resolution, some content will need more bitrate than others to achieve the same quality level. The best example is a sport game vs a news interview. If the static news interviews is okay at 500Kbps, the sport game with lots of action, fast moving camera and scenes cuts will be horrible.
What I understand is that you want to encode each of your files, whatever the content or resolution, to the maximum perceptible quality. Instead using an average bitrate for video encoding, you should use a constant quality index.
01. Download the last nightly build of handbrake for your system at
https://build.handbrake.fr/
02. In the video panel, encode it using "Constant Quality" with an RF value around 19 to begin with.
03. In the advanced panel, max out all the options and disable mb-tree.
04. Review the encoded video and lower the RF value to 18 to increase quality or increase it to 20 to lower the quality until you find the right spot that please you.
05. Don't look at the bitrate, ignore it.
You don't need to go insane with the encoding options because at a point you will get about no quality increase or file size decrease. Some good options to use are :
b-adapt=2:rc-lookahead=50:ref=6:bframes=6:direct=spatial:me=umh:subq=10:merange=32:psy-rd=1.0,0.10:analyse=all:trellis=2:no-mb-tree=1
In the advanced panel, paste them in the x264 advanced option string and adjust the quality slider in the video panel. The video might not play on mobile devices as I don't see it as a requirement in your post.
As the video is scaled down there will be less noise and artefacts in it so an RF value of 19 can be low (too much quality). Note that I mainly use RF 16 for a 1920x1080 video to retain more grain and quality but some will always tell you that it's too high or too low...
Eric