Well said, Latexman.
RJB32482: The important thing to remember is that the opening force on the valve is caused by the differential pressure from upstream to the discharge, applied against the area of the seat. The spring load is equal to the opening force at the set pressure.
If you superimpose a back pressure, that will raise the set pressure by the same amount. It is then possible for the "protected" vessel to exceed its MAWP if the superimposed backpressure is high at the time of a process upset.
The Bellows effective cross-sectional area is the same as the area of the seat. The bellows is vented to atmosphere, which is relatively more constant-and besides, the MAWP of the protected vessel is measured in gage pressure units. So with the bellows referenced to atmosphere, there is no effect upon the setpoint with variable backpressure. There IS STILL an effect upon capcity that should be evaluated. With a lot of backpressure during discharge you may experience enough flow restriction so that the pressure continues to increase above the "BOOM" value.