Why does wire gauge go down as the physical wire size goes up?
A seminal empirical definition of wire gauge was the number of times the wire had been passed through a draw plate.  Each draw plate would reduce the diameter of the wire by about 10%, therefore the more it had been drawn (higher gauge) the thinner it would be.

Geometric approaches such as AWG define a ratio between wire sizes (AWG uses a ratio of 0.890526).  Thus, a 31 gauge wire has a diameter 0.890526 that of a 30 gauge wire.  This correlates roughly to the empirical definition.

It gets more complicated with stranded wires, but this explains why larger gauges mean smaller wires.  (Shotgun shells work the same way.)