sink, submerge, addicted to
沉 centers on sinking down into something: physically submerging in liquid, or metaphorically being deeply absorbed or addicted to something.
沉 is a variant form of 沈, combining 氵 (water) with 冗, which likely contributes a phonetic element. The exact historical development of the 冗 component in this character is uncertain.
Water 氵 on the left and a shape like a person sinking under a cover 冗 on the right: imagine someone slowly submerging into deep water, becoming completely absorbed.
For チン, picture a heavy chin sinking into water: chin -> チン, and the weight pulls it under.