I would make sure you are able to explain what and how you have taken on more responsibilities etc, and also that you've taken the opportunity to review your finances and that to be able to do the things you want to do you would need to be on $x - as such are you able to be moved up to $x.
If they say no, then you can ask what it is that you need to be doing to be able to justify that level of pay, and when can you start
IMO it's a more pro-active way of asking for a pay increase plus even if they come up with some excuse not to give you more money right then you are ready and able to pin them down to criteria which can be used at a later date to justify a raise.
It also raises the point in the managers mind that although you are happy now, you are open and ambitious enough to be considered for opportunities for more responsibility and therefore better pay - which means that your name will be one discussed when positions like that come up but also it puts the thought in the managers mind that you have ambitions and that if the current company doesn't meet them then you will be looking elsewhere - but in an assertive and cooperative manner.