Weight and balance is one process: every bag is scanned, and pit location recorded, every LD-2/3 container is weighed and its location on the airplane recorded, every passenger is accounted for, fuel load and distribution is measured and accounted for. Central load planning calculates weight and balance, then that information is uplinked (data link) into the FMC.
Takeoff performance is another process: it considers, aircraft weight, CG, runway length available (intersection departures are common), runway elevation, slope, surface and condition, height of terrain and climb required after takeoff, air temperature, wind direction and speed, use of engine anti-ice, flap setting, and any deferred/inop items on the airplane, such as a thrust reverser, or a brake (with 8 brakes on a 767, you can go with one inoperative, though it's rare). The critical numbers: V1 - decision speed, Vr - rotation speed, and V2 - safety speed, are uplinked into the FMC, and displayed on the PFD, as well as set using "bugs" on the airspeed dial on a 757/767.
Takeoff performance, particularly in a place like Eagle, CO, takes into account far more than just the airplane and the runway. The environmentals and the climb after takeoff, including engine-out climb, are all considered.
In general, we use reduced thrust for engine life and reliability.
The greatest stress on the engine is when it's making full power (like takeoff) and it's rotated in pitch (like takeoff). The combination of thrust load and gyroscopic load is the most the engine will see in the entire flight, so reducing both of those loads helps the engine avoid a catastrophic failure at rotation, which is when most failures occur. That's the reliability concern.
The life concern has to do with thermal stress on the blades/casing/stators in the hot section. The last few percent of RPM and thrust put a LOT more heat into the hot section. Reducing thrust by 10% can reduce the thermal load by 20% or more and keep the engine in service for longer.
We use full thrust when required: contaminated runway (snow/slush), in strong, gusty winds, when windshear is a possibility, or if it is required when the above analysis is completed. Often, the subsequent climb on one engine is the key factor that necessitates a full thrust takeoff.