You lose quality every time you save a jpeg file: JPEG is what's referred to as 'lossy compression'.
But that's okay - with the original file size you describe, the image is, for your purposes, as good as a losslessly compressed one.
What makes JPEG compression 'lossy'?
Simply put, JPEG reduces the detail of the picture, attempting to reduce the kind of detail that is the least noticeable to a human person. With higher quality settings (resulting in larger file sizes), the loss of detail may not be noticeable at all. With lower quality settings (resulting in smaller file sizes), it will reduce fine details (like small leaves in a tree, hair, freckles) and introduce compression artifacts (well illustrated in the Wikipedia article on JPEG).
When you open a JPEG, it is decoded (because the program does the editing on an uncompressed copy of the picture in the computer's memory), but that doesn't make the picture quality any better: If you open a low-quality JPEG in your picture editing program, the artifacts stay and the details remain lost.
If you save the picture again, the program takes the uncompressed picture from its memory, and applies another round of JPEG compression to that picture with all its artifacts and lost detail, getting rid of more detail and introducing more artifacts.
So if you compress an picture at high-quality settings multiple times, each compression will reduce the picture's quality. There are YouTube videos that demonstrate the results of repeated JPEG compression.
What's been lost stays lost forever, and each round of compression adds to the loss - a little loss for high quality settings, a lot for low quality settings. Even if you open a highly compressed (low quality settings) JPEG and save it again with lower compression (i.e. higher quality settings), you'd get a larger file with lower quality.
Why is JPEG still 'Good Enough'?
As I said in the beginning, all is not lost for what you're doing. While it would be preferable to get pictures in a RAW format (losslessly compressed from the camera's chip), this is far more important for changing the brightness or colors of the image; retouching a picture suffers far less from previous lossy compression.
I wouldn't obsess about files sizes too much. The file size of the original picture may simply be way overkill, with a little more compression still producing virtually identical quality. (Of course this is good for you, as the picture you're editing hasn't lost any fine detail or introduced any artifacts yet.)
Experiment a little with different JPEG compression options, and you will probably notice that with high enough quality settings (e.g. 90%) you'll get good results - the quality of the original image won't be noticeable decreased, even if you zoom in and compare specific parts of the image.
RAW editing adds another layer of complexity to editing pictures too - not least of all because you'll need a different program, as GIMP can't do RAW if I recall correctly.