When I upload an article picture in the K2 image tab, it more than doubles in filesize when you view the image in an article. When I upload the picture via the Joomla media manager and use the browse server option in the Image tab the filesize stays the same. I only talk about the filesize here. The dimension, resolution etc. stays the same.
Is this maybe a configuration problem or a known bug?

Check your K2 Parameters. On any K2 page, click on Parameters on the top right. Under images, you can change the default sizes. You'll have to reupload the image after you change the sizes.

@ovsovso

As Vinny Hebert check the image options in K2 parameters. Apart from the size options take a look at the quality option. This affects also the result image file. Finally note that PHP is not designed for resizing images. It cannot achieve the optimization level a tool like Photoshop does. Joomla! media manager is a different story since it does not resize any images. It just uploads the image as it is.