If I understand your question correctly, that you want to be able to dynamically increase/decrease the size of the object as it moves along the x-axis, I recommend that you use $('#changeMe').offset() inside the jQuery UI drag event.
You can create a formula that you want to use based on an initial offset, and the new offset to size your container by $('#changeMe').css({ width: X, height: Y });, and insert whatever your X and Y values are in pixels.
Edited for further elaboration with code:
var initX = 0;
var initW = 0;
$('#changeMe').draggable({
start: function() {
initX = $(this).offset().left;
initW = $(this).width();
},
drag: function() {
var deltaX = initX - $(this).offset().left;
$(this).css({ width: initW + deltaX });
}
});
If you used that as your base, it's a very nice and simple solution for your application.