Because you are potentially dithering the image, and a dither adds more information.
My explanation about compression.
"Imagine you have a gradient, from left to right, from white to black."
That is it. I just told you the compressed version.
Here is the uncompressed version:
"One pixel white. Next pixel not as white, next one a bit darker, next one a bit darker than before, next one...
On the second row. First pixel white, next pixel..."
Now, A gif image dithers the colors to emulate a gradient.
"First pixel white, second pixel a little gray... Next pixel... Ouch... as I do not have another gray, lets put a white pixel again to emulate a lighter combination of the gray pixels around me".
When you convert the image again to JPG... You do not have a gradient anymore you have the mess the other dude... I mean the GIF Made:
"First pixel white, second pixel a little gray... Next pixel... Ouch... that dude made a mess of the file... Ok, let's copy that mess... Second pixel little gray, next pixel white..."
So. Please STOP converting to GIF. Do not use it. The only valid case to use a GIF on the XXI century is an animated GIF.
Understand the file types needed for website design.
PNG for flat images or transparent ones.
JPG for photos.
SVG for vector shapes.
GIF for animated images. Flat design strongly recommended.
MP4 for video.