border, boundary, staircase, hundred quintillion
垓 centers on a boundary or limit: a border, an edge, or the end of something. The staircase sense is a stepped boundary, and the huge number sense (hundred quintillion) is an extension of a vast, distant limit.
垓 combines 土 (earth) with 亥, which likely contributes the sound. The original meaning is a boundary or limit, often marked by earthworks or steps.
The earth radical 土 beside 亥 suggests a raised earthen boundary or a stepped embankment. Picture a staircase carved into the earth marking the edge of a territory.
For ガイ, imagine a guy standing at the border of a vast field, looking out at the hundred quintillion stars: guy -> ガイ, and he marks the boundary.
10^20; 100,000,000,000,000,000,000; hundred quintillion