Hawaiian volcanoes get older northwest of the Big Island. What records that?

Answer: Plate motion over hotspot

Plate motion over hotspot ✓ — Right. The plume or hotspot is relatively steady while the Pacific Plate moves over it, so old volcanoes are carried away and new ones form above the heat source. USGS gives the Pacific Plate motion as about 6 cm per year. A chain of islands becomes a slow-motion speedometer for a plate.

A westward lava river — Lava does not flow thousands of kilometers and then freeze into a timed island chain. Individual Hawaiian flows are local; the age pattern comes from plate motion over a heat source. The useful clue is that the youngest volcanoes sit near the active hotspot, while older seamounts trail away.

Erosion choosing old rock — Erosion changes the height and shape of old islands, but it does not create the age progression. Kauai is older and more eroded because it has been carried away from the magma source longer. Erosion is the after-effect; plate motion is the clock.