Why does 2001 Chevy Tahoe steering sometimes gets hard to turn to both sides and gets easy when accelerate?

The Power Steering output is directly proportional to the engine speed [RPM]. I suspect that when it is difficult to turn, the engine is at idle speed, which is set too at too low an RPM. Then when you depress the accelerator, the engine speed increases and the power steering pump speed and output power increase also. Have a qualified mechanic check and properly set the engine idle speed to the manufacturer's specifications. IF the idle speed is not abnormally low, would suggest a badly worn power steering pump. Properly set idle speed first, and if that does not correct the problem, then have the power steering pump output checked.