will this break my xbox360?

idk but its not good for it to run that long. How much weight did it lose?

I had a the original white Xbox and I uses to use for days at a time without powering it off and it still runs great. I now use a mw3 slim Xbox and it is supper dusty and Is always, ALWAYS running and none of my disc have problems. It hasnt been turned off in over a month! The only problem I get is slower loading times in when opening the guide or sifting through my settings tab. I wouldn't suggests using it a lot so try to keep down its usage but if you so use your Xbox to much it will damage something's so make sure you clean it's fan from time to time and clean the dust out of its filters.

by break do you mean fall apart no!!

but you could get the red ring of death

or the xbox will over heat and you will have issues later in time

It might cause it to overheat and fry wires or laser burn your games and it could also lead to the red ring of death