metadata - If an image is rotated losslessly, why does the file size change?

I was searching for methods of lossless image rotation and happened upon this question which explains it rather nicely:

Are "Windows Photo Viewer" rotations lossless?

So I created a 256×256 JPEG with random pixels (Photoshop cloud filter) and then rotated it using Windows Picture Viewer. After rotation, the file size actually increased, but only on the first rotation. Every subsequent rotation thereafter, the file size remained static. I know it's rotating losslessly because I've rotated it multiple times with no noticeable quality loss whereas a 257×257 image being rotated 20 times became very lossy.