Your Weller is alright, but not for electronics. As the product description states,
[...] optimally used for heavy-duty soldering, cutting, and smoothing applications including those involving: heat sinks, ground plans, metal art, and plumbing. The 9400PKS is also acceptable for use on hobby models, small appliances, small engine repairs, crafts, audio systems, electrical, marine, jewelry, and automotive.
This gun is not recommended for use on micro-components, electronic kits, low voltage wiring, PCBs, radio-controlled devices, or indoor lighting.
If you want to do electronics, get a temperature-controlled iron. In your present project, the capacitors may be connected to large ground planes, requiring to be heated for a while at full power to get them up to the solder's melting temperature. But then the power needs to be dialled back, to avoid damaging the PCB. That's what closed-loop temperature control is for.
Having said that, I'd suggest you toss that graphics card. Who knows what agonies the original owner has it put through; and you know what
you have put it through three years ago...
EDIT: Yep, the KSGER you just bought is a better choice for electronics.
Now on to the next step, dump that graphics card.
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