Hi Grant

If you wish to see no change in spring load/movement for changing pressure
you have to set "Pressure Stiffening" (at caesar setting Tool-Computation control) to "NO" in case you are using metallic piping with caesar default setting.

By default caesar consider
1)Bourdon force off for metallic piping
2)Pressure Stiffening as per Appendix D B31.1/B31.3 note-7


Regards

Habib