That's not a simple question. The first order approximation is that CURRENT is what creates the magnetic field that saturates the transformer. If you put a scope current transformer on the primary, load the secondary with the resistance and inductance of your welding setup, crank up the voltage until you see a sharp rise in the slope of the current pulse. That's the too-much point. What happens when you add more caps is dependent on the transformer characteristics. Energy is linear in caps but quadratic in volts.
25 years ago, I was tasked with fixing an OEM forward converter that would randomly self-destruct. I built a fixture to synchronize the load transient with the switching frequency. I could watch the primary current head for the sky on the scope as the load transient crossed the switching point. Took it to the vendor site and proceeded to blow up power supplies until they conceded that they had a board layout problem to fix.After the weld, the field will be sitting somewhere on the B-H curve of the core. The next weld might be very dependent on where you left it last time.
This is a page from my Unitek CD spot welder. Shows how they reset the core.
I experimented with a microwave oven transformer battery tab welder. I was hitting it with a timed pulse. Repeatability was horrible. When I synchronized the pulse with the line and gave it an integral number of full cycles, the starting point on the B-H curve was consistent and the welds got much more repeatable.
There was considerable discussion on exactly when you should terminate the pulse, but mine was constrained to somewhere near zero current by the triac.