How do I make my wordpress post appear in a mouse hover preview?

I would separate your PHP and Javascript.

Run the loop as you normally would, but instead of showing it on the page wrap it in a div with a display:none;

Make sure to give each post an id that you can identify against and then on whatever you’re hovering over could have a rel, with the same id. then your jquery hover would be more like…

jQuery('.hoverGuys').hover(function(){
    theIDIneed = jQuery(this).attr('rel');
    jQuery("#"+theIDIneed).show(); // this is the simple example, you might want to use clone
});