I'm sure others will respond - especially
@thebestcpu who has the best expertise - but jpg is a lossy format. That means each time you
save and reopen the file, you will lose quality. You can make multiple changes within your editing software, even saving it while keep the file open and working on it, and you won't have loss of quality. It's when you save, close, and then reopen that quality is affected.
Constantly resizing also has an effect. One method I've read about is to make your image a smart object and details will be preserved within the editing process. It does get sticky since adjustments can be limited when using smart objects. But again, saving, closing, then reopening does its damage. Also saving it at the same quality level does not prevent loss.
How big is the loss of quality? As most things in life, it depends. There is a loss of detail and also depth of color. It actually might not be that noticeable. I would think that if you open your original, open a copy, and compare side by side, you can get a visual on what the loss is. Zoom in and look at your edges as well.
If you're doing ongoing work with an image, it's always best to save as a tiff or png, both lossless formats. BUT - why are you reworking jpg's? Why aren't you saving as a psd file? You can print from a psd file unless you're sending the file to a print service that demands a jpg. If that's the case, you can alter your psd file, do a "save as" for the jpg, then close the psd file without accepting changes especially if you're just resizing.
Any prints I produce on my own printer are from psd files and I always indicate on the print setup that Photoshop manages the colors.
I'm certainly not the last word on this and hopefully others will weigh in. But it seems you're aware of jpg limitations and follow the workflow that works best for the image.
- Jeff