Put simply, the engines work most efficiently at a certain number of high revs per minute. If, in your example, you remained at FL350, as the mass of the aircraft burned off, to maintain your cleared Mach number, you would have to reduce power into a relatively inefficient regime. In order to get the engines back into their most efficient revs per minute, you request climb clearance into thinner air.
Good answer, though not to the question the OP asked.
Still, now he knows both why you are
able to climb higher as you burn off fuel and also why you would
want to.
