The weld gun pressure is used for two main reasons to hold the parts together tightly during the weld and to provide forging action during the weld and cool down phase. The hold together includes containing the weld nugget and flash from the faying surfaces and the electrode contact areas. Any adjustments to pressure would be made to facilitate these functions and improve or lengthen the life of the electrodes.
One must always remember that for every action there can be reactions. A change in the pressure can change the heat being generated and thus cause the nugget formation to increase or decrease. This is discussed in an article in this blog titled:
HOW WILL TOO MUCH PRESSURE AFFECT RESISTANCE WELDING?
This article demonstrates that increasing the pressure will decrease the contact resistance. Therefor with the same current flow the total heat in the part will decrease. If the heat is decreased the nugget size will not grow and it is likely going to decrease in size. If the goal was a smaller nugget increasing pressure might work.
If one were to decrease the voltage at the same time by dropping the transformer tap or adjusting the control settings, this would reduce the current flow. Now we have lowered the total current and the resistance is lower due to the increased pressure.
Joules law states that heat is generated by:
Lowering the current and resistance at the same time would greatly decrease the heat being generated at the faying surface. Lowering the voltage when the pressure is increased is not a good parallel adjustment. Increasing the voltage might be a better move if the nugget needs to be maintained after the pressure change.
Adjustments to pressure may be necessary to maintain proper containment of the parts. If the pressure changes affect the weld nugget then changes to the current would be necessary to compensate. To drive more current more voltage would be required.
If indentation is excessive maybe less pressure might be applied. If the nugget is not affected all is good. If the nugget is out of tolerance after the pressure adjustment, then adjustment to the current might be needed to maintain proper nugget size.
References: RWMA – Resistance Welding Manual 4th Edition