What is nominal n1 and fuel flow behavior during cruise climb?
 

For a commuter airliner (e.g. 737) performing a cruise climb (step climb) at a constant Mach, how should n1 and fuel flow behave?

I know that fuel flow should decrease with altitude (air fuel ratio). Should fuel flow also decrease with weight (fuel burn off)?

Is n1 kept constant? Does it decrease with weight? Is it unaffected by altitude?

If it depends, then what systems (fadec?) or settings (rated/non-rated mode?) are responsible for setting the behavior.

Fuel flow will decrease with aircraft mass, all other factors being constant.

(As an aside, the 737 is not a "commuter airliner".)

Actually the fuel flow will increase as the engines spool up to climb power. However, the fuel flow will decrease with the weight if comparing two different AC weights in the same condition.

N1 CLB power will increase with altitude due to the air being less dense at altitude.