Currently Being ModeratedDec 4, 2012 7:05 AM (in response to geordyvarghese)
You post seems to suggest you are backing up using the internal HD. If that is the case it is unwise; back ups should be separately stored. Buy an external HD, say 500GB, back up what you need to that then clear your surplus backups.
I don't a have MacBook Air so I am not sufficiently familiar with the machine to advise how to do that.