@Georgiy Ivankin made a suggestion in a comment, I used it successfully :) -- , but with slight changes:
$('#note').on('keyup',function(e){
var maxHeight = 200;
var f = document.getElementById('note');
if (f.clientHeight < f.scrollHeight && f.scrollHeight < maxHeight )
{ f.style.height = f.scrollHeight + 'px'; }
});
It stops expanding after it reaches max height of 200px