Why do airliners on autopilot climb during cruise? Several years ago I was a passenger on a near cross-country flight when the pilot came on the PA and announced that we were climbing towards our cruise altitude, on autopilot, and as our fuel load was burning off, and the plane's weight lessened, we would be climbing about another five thousand feet from our cruise altitude.  

I wondered why the autopilot, instead, would not make micro-adjustments to the angle of attack to maintain the same altitude, rather than waste fuel making an unnecessary climb. 

I realize that maintaining the same exact altitude is probably not realistic, but autopilot, I would think, ought to be able to maintain cruise altitude within about one thousand feet. 

This was on a Southwest flight, so it had to be a Boeing 737.
Climbing further while cruising is saving fuel, not wasting it.

First, every airplane has an optimum angle of attack for most economical cruise. If it loses mass (due to fuel consumed), it needs to adjust either its altitude or its speed to keep that angle of attack. The goal is to keep dynamic pressure, the product of air density and the square of airspeed, constant. Since you want to reach your destination in the shortest time, climbing into less dense air is the better option.

Secondly, gas turbines need less fuel per unit of thrust when flying in colder air. As long as the plane stays in the troposphere, it will fly more economically when it flies in colder air.