JPEG is a lossy format and it has variable quality levels which result in larger or smaller file sizes. Whenever you save a file in a lossy format, additional detail is lost, so even though you saved the finished version as a higher quality JPEG, it is still actually lower quality than the original was, despite the growth in the file size. It is still closer to the original image than it would have been if you had used a lower compression quality and re-compressed the image.

Put really basically, JPEG is trying to fit an image to a pattern. The lower the quality of the compression, the more looser the fit is allowed to be, which reduces the file size, but also means more detail is lost. Conversely, a high quality requires that the compressed file much more exactly match whatever you had originally opened, but means that the file also must be much larger.

One other way to think about it is that the actual data held in a JPEG, uncompressed, is much larger than the size of the JPEG. You can open a very highly compressed image or a very slightly compressed image, but both actually have the same number of pixels with the same bit depth, which takes far more space than compressed file size. When you choose a higher quality, you get less compression of that large amount of data than if you use a low quality/high compression setting.

This is one of the reasons that it is best to shoot RAW if you plan on doing post production work on an image because RAW generally does not use lossy compression and will preserve the quality of the image until you are done with your manipulation and ready to make a final export of the image.