increase, add to, augment
增 centers on making something larger in amount, number, or degree: increasing, adding to, or augmenting what already exists.
增 combines 土 (earth) with 曾, which likely contributes the sound and the idea of layering or adding. The character expresses increasing or augmenting, perhaps originally by piling up earth.
The left side is earth 土, and the right side 曾 suggests piling up. Picture adding more soil to a mound, increasing its size layer by layer.
For ゾウ, imagine a zō (象, elephant) adding its weight to a pile of earth, making it increase: zō -> ゾウ.