Can I change to bigger tires? I have tires that are fitted to my bike and are 2.1, because of this my rim is quite thin. Will I be able to change to 2.4 tires or will my rim be too thin. If so can you suggest a good rim size?
Generally you can fit a range of tire sizes on a given rim. 

You might be able to put a 2.4" tire on your rim, but you should research the rim manufacturer's recommendations for tire sizes that will fit your specific rim.

This compatibility chart from WTB suggests that a rim with internal width of 25 mm (measured across the inside of the rim sidewalls) is the only one that can be used with both a 54-mm tire (2.1") and a 60-mm tire (2.4"). Again, this might not agree with your rim's manufacturer.