Why fly nose up?
On most aircraft the wing is set about 1 degree up relative to the fuselage. At the start of the cruise when weight is high this will leave the fuselage a bit nose up. As weight reduces it will come down a bit. The general idea is to keep it aligned with the airflow as far as possible over the whole flight, however flow over the fuselage generates a bit of lift which is in the right direction even if the fuselage isn't as good at the job as the wings. If it was aligned with the flow at the start of cruise it would be pointing down at the end, generating both negative lift and positive drag.