What happens to output if OPAMP its supply is tweaked?
For an ideal op amp, which has zero input offsets and infinite gain, nothing happens.

For real op amps, the output will change slightly with changes in the power supply voltages. The ratio between the supply changes and the output changes is called the Power Supply Rejection Ratio (PSRR)or Supply Voltage Rejection Ratio (ksvr). The ratio will vary with op amp, and to make things more complicated the number for any op amp will vary with frequency. Higher frequency supply variations will produce a greater output variation than lower frequencies. 

In general, for low frequencies, the rejection ratio will be on the order of 80 to 100 dB.