I have a Nikon D3300. RAW images are usually 25-28 MB at a resolution of 6000 x 4000. I exported from Lightroom at Quality: 100; DPI: 240. The exported JPEG turns out to be around 12 MB. I took the same RAW file and this time bumped up the DPI to 600. It turns out, both images are exactly the same file size.
I was anticipating that a higher DPI setting would mean larger files. Higher DPI = more dots per inch = more information = bigger files. Why is this not the case?
An image doesn't have a DPI until you print it.
All it has are dimensions in pixels.
Anything else is simply an interpolation of one system to another in order to display on your screen... which is probably about 72dpi anyway.
If your image is 6000 x 4000 pixels, then that's its size, whatever dpi you think you may have saved it at.
The only time DPI comes into play on your computer is if you paste into any word processor or page layout app, when the DPI is used to decide how large the image will be when printed.
(extrapolation of my post at https://photo.stackexchange.com/a/93405/57929)
Higher DPI = More dots per inch
You are on to something here. DPI relates dots and inches. Where your understanding is incorrect though is in thinking that by increasing the DPI value that you are somehow "adding" dots, or pixels, to the output. No. Your resolution is fixed, at 6000 x 4000. Changing the DPI setting changes not the dots, but the inches at which your image will print. Whatever the DPI setting, the number of dots in your image remains constant. So the constant file size is what would be expected.
Many people misunderstand DPI to be some kind of "quality" setting for exporting images. Really it's irrelevant. What you should care about here is total number of pixels.
The DPI value stored in an image file is only a hint to any printer drivers regarding how large to print the image - e.g. at 600 DPI, your 6000x4000 image will print at 10" x 6.67", while at 240 DPI, it would print at 25" x 16.67". The resolution of the image remains 6000x4000 in either case, so the image file remains roughly the same size. To create a smaller file, you need to resample the image to a smaller resolution, e.g. 3000x2000 should give you a roughly 4x reduction in file size, at least for uncompressed formats - JPEG might do better or worse depending on the actual detail level in the image.
A very important exception to "dpi is just instruction to printer about how to space the pixels". Which is very true for the printer, however to a scanner, if you scan to create a picture at high dpi, the data file will be much larger than if you scan it at low dpi.
"300 dpi" to the scanner is instruction to create 300 pixels per inch scanned (affecting size of data, but not size of print). More dpi is more pixels. But if you scan 4x6 inches at 300 dpi, and print it at 300 dpi, it will print 4x6 inches size. If you print this picture at 600 dpi, it will print 2x3 inches size on paper.
"300 dpi" to a printer is instruction to space the existing pixels on paper at 300 pixels per inch (affecting size of print, but not size of data). More dpi is a smaller printed picture. Then it would be printed at the higher dpi number (spacing of pixels on paper).
However color printers generally cannot show an improved picture at much more than about 300 dpi (printing is designed for the human eye to view). They have to try to show 16.7 million possible colors with only perhaps 4 colors of ink, so they have to dither many dots to try to simulate one color, which simply won't all fit into a tiny pixel space.
So if planning to proceed, you should try some tests, and really ought to confirm that you can actually see whatever you choose to believe.
