My paver patio in Nashville sank 2 inches on the west edge after one hard rain
I put down 4 inches of base on the west edge but only 2 on the east because I got lazy with the tamper, and now I am wondering if I should pull up the whole thing or just lift that corner and re-sand it?
Lifting just that corner won't fix the real problem, which is that your base is uneven and too thin on the east side. That 2 inch base is going to keep moving every time it rains hard, so patching the west edge is like putting a bandaid on a broken leg. The sand between the pavers does nothing for support, it just fills the gaps, so re-sanding that sunken corner gets you level for maybe a month. Pull the whole thing up and fix the base right, 4 to 6 inches of compacted gravel everywhere, no shortcuts. It's a weekend of work you don't want to do twice.