I think you mean that the background image isn't scaling.
You could use the css command "background-size" to solve this problem..
Values that could help you are "cover" or "contain": http://www.w3schools.com/cssref/css3_pr_background-size.asp
var target = $$.css('background-image').replace(/^url|[\(\)'"]/g, '').css({ 'background-size': 'cover' });
If this is not working, you could read out the actual absolute width of your image an set it as background-size. But then you need an resize-event for when you're scaling the browser window..
I would recommend to use two pictures and show/hide the pictures instead of using a background-image for the hover.