The link leads to a 404 error.
Check the scale rate of your layer. (Select the layer and check the "Properties" pannel)
Default value is 100, less or more can end up in changing the size of the images displayed on it.
And if you have set "Parallax in editor" to yes, that may be what is causing the background to be "non working".
As for "importing huge image", that's mostly a bad practice.
C2 aims at games for the web, so it's generaly a bad idea to import a huge texture, it will end up ruining performances on lower hardware.
Break down the big image in several other smaller one that you can reuse through the game.
It will also lower the download size which is a good thing from the player's point of view.