Why does GIMP increase the size of exported JPEG files?

A difference between the settings used by GIMP and your digital camera likely explains the change in file sizes you're seeing. By default, GIMP appears to export JPEGs with quality 97 without subsampling. Many older digital cameras may use quality settings around 80-90 with subsampling. Using the first photo I encountered on my computer, saving with Q=90 + 4:2:2 subsampling resulted in a 3.9MB file. But saving with Q=97 + 4:4:4 subsampling resulted in a 14.1MB file. The change in file size is about 3.6x.

To maximize efficiency (lost data vs change in file size) when resaving JPEGs, it's usually preferable to use settings that are as close to the original as possible. GIMP has an option to facilitate this: Use quality settings from original image.

• For details, see What factors cause or prevent "generational loss" when JPEGs are recompressed multiple times?

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When exporting to JPEG, there are several settings that affect file size. The primary settings to consider are in bold.

• Quality. Digital cameras usually use a setting similar to 94-98.
• Arithmetic coding. Don't enable this setting. Such files will not work with most image viewers or web browsers.
• Subsampling. Digital cameras usually use "4:2:2 horizontal (chroma halved)". Pick the option that halves the longer dimension.
• Optimize. This just optimizes some compression internals. Doesn't hurt to enable. Space savings are moderate.
• Progressive. Better to leave it off. Space savings are minimal, and files take longer to decode.

It seems that GIMP is not able to guess the appropriate compression settings for your photos and artificially boosts the "quality".

Don't let the "Use quality settings from original image" option deceive you. Unless the original JPEG is saved by the same library (and in your case, it is not, because it was produced by the camera firmware) the quality parameter is just a guess. This means that using smaller quality settings does not necessarilly mean that we are compressing the image more than the original, especially when the original was created by a different code. Increasing the file size by a factor of 3 is a strong hint that the quality parameter is too high.

Your editing (increasing the contrast and saturation) makes the image less compressible for JPEG so the file should be just slightly bigger. Simply decrease the image quality during export until the file size is reasonable.