Sounds like it's low on gas. The faster you turn it, the lower the suction pressure is because the compressor pumps harder. At idle the gas that you do have is enough to keep the low pressure switch made. At some certain RPM the suction pressure drops enough to break the low pressure switch. The compressor shuts off, the system equalizes, the low pressure switch makes again, thus the cycling. A restriction (plugged orifice tube or/and expansion valve) will cause the same symptoms.
2000 Sierra 2500 HD. 408 (11-2007) Whipplecharged, Big (18x24x4) FMIC.