Your most indispensable "tweak"?

I wired in a double pole double throw switch to sometimes bypass my sub crossover.  This allows a lot of harmonics to be added to old LP recordings that are otherwise terrible sounding.

A well implemented tone control in preamp stage.
Not to fix sound of system—rather, to tweak/render bad recordings listenable.

My tweaks involve a soldering iron and only the amplifier.

1. Replace the Schottky rectifiers in my amplifier's power supply with SiC rectifiers.
2. Replace the Mundorf interstage capacitors with Jupiter copper foil caps.
3. Replace the volume "potentiometer" with a stepped attenuator.
4. Replace the stock output transformers with Lundahl transformers.

The  audiodharma Cable Cooker is well worth the cost. Really improves my cables and also gets rid of the break in period for new wires. Perfect when I get back from vacation as well.
If you want to see if a new cable is better, just cook it and you know right away.

Of course, the real tweak is Super Audio CD.  The extra cost for a SACD over a CD is tiny compared to the improvement in sound.

@testpilot 100% agree.  Unless cabling is considered equipment and not tweaks.  In that case, Hallographs and SR HFTs are most cost effective and necessary acoustical room treatments.