you can you jquery focus function , that when mouse move to your textbox and click this method fire!
this link work better than your Idea,when the character length go bigger the size increase!
http://www.jacklmoore.com/autosize[
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and this is the focus document event on jquery website:
api.jquery.com/focus[
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and this is an example of the script you looking for:
<script type="text/javascript" src="https://www.google.com/jsapi"></script>
<script>
$(document).ready(function(){
$('textarea.expand').focus(function () {
$(this).animate({ height: "1000px" }, 500);
});
});
</script>