I’ve been on Southwest flights so sparsely full (maybe 40 people on a plane with capacity for 120) where the flight attendants have to repeatedly tell people to “spread out for weight and balance.” That’s about as scientific as their calculation got.

Which is drastically different from my experience from flying a different carrier with a very empty plane. The original seat assignments had all of the passengers bunched together and the flight attendants denied anyone's request to move to empty rows until the plane reached altitude. They finally explained that the plane's load master stated that's where the weight needed to be during take-off/landing. Once they explained that, everyone complied without any further complaints.

I wonder if everyone moved back to their assigned seats before landing. Did they?

Yes, when they made the announcement about making the descent on approach, they asked everyone to move back to the seats they were in on take off while return your tray and seat to their upright position

CG CP - Center of Gravity, Center of Pressure.

I just took a nearly empty southwest flight last week. The flight attendant asked me to move further back in the plane, and appeared to have an iPad or notepad she was using to track passenger count per zone. First time I’ve seen this system.

For most flights, it is fine, since most SW flights are full or close to it. It is for the flights that happen at off times to less popular destinations where you may have a half empty plane with most people toward the front, to one side (to see a view maybe), etc.

Passengers are (for the most part) considered equal for W&B calculations. It's about "Is this seat occupied?"

Southwest uniquely allows passengers to board the plane as they please. Random boarding is mathematically the faster way to board (where other airlines choose the slowest options to drive priority boarding upsales), but has this side effect.

When an airline does need the passenger's weight, they don't ask. They measure, and oblige the hand baggage.

It's common in the Pacific, as there are many small islands connected by planes.