Try this (demo):

$(function() {
    $('acronym').hover(function() {
        var tip = $(this).attr('data-tooltip') || $(this).attr('title');
        var tiptip = $(this).text();
        $(this).attr({
            'title': '',
            'data-tooltip': tip
        });
        $(this).append('<div id="tooltip"><h2>' + tiptip + '</h2>' + tip + '</div>');
        $('#tooltip').fadeIn();
    }, function() {
        $('#tooltip').remove();
    });
});

Basically we store the tooltip in a new attribute "data-tooltip" instead of saving it back into the title. The first line should work like this: the first time it sees it, there is no "data-tooltip" so it is undefined, so the "||" (or) goes to the next item which is the title. We later save the title into the data-tooltip so all subsequent times the first line is encountered, the data-tooltip is defined and it never continues to the title. I hope that makes sense.

The data-tooltip is a valid attribute in HTML5. Anything with data- in front is valid. I could have just as easily saved the tooltip title into the element's jQuery data.

The reason fadeOut isn't working is because the #tooltip isn't unique. If you unhover the element with a tooltip and immediately hover over another tooltip, the tooltip div has fadeIn() applied as soon as the content changes. You could make a unique tooltip id for each element, but it could get messy if you don't make sure the tooltips are removed - which I've seen happen if a user goes crazy nuts hovering and unhovering numerous tooltips.