The Air conditioning in my 07 GMC Sierra seems to be robbing more power than usual from my motor. I recently replaced the blower motor resistor and it was around the same time that the resistor went out that I noticed this problem.

(Cont'd) If the A/C is on and I have cruise set on the interstate when I hit an overpass the trans will downshift to try and keep speed, this never happens when the A/C is off and it never did it with A/C on before. What could cause this? I don't want to pay the shop $50 just to put it on a machine until I've checked everything I can myself.

the a/c clutch may be the issue. Try turning it by hand with the engine off and see if it is binding up

As the reply states above, the compressor/ or clutch may be mechanically starting to bind and load the engine.
I would check the refrigerant charge. If the unit is over-charged or if it has air and non-condensables in the system this will run the discharge pressure(Head/highpressure side) up which will put a heavy load on the vehicle engine. With gauges hooked up check the high pressure side to see if it has an excessive pressure...300 psi plus.
Also if the unit has an over charge of refrigerant this can also lead to a excessive mechanical load on the engine and can lead to compressor failure dur to liquid flood back. You suction should be no more than about 45 psi and adverage around 30 psi once the vehicle has cooled down in the passenger compartment. The suction line should be cool and sweating. If excessively cold, this is a good indication that there may be a refrigerant overcharge.
At the cost of the refrigerant and compressor , it would be worth having a certified tech test your system.