Green’s Dictionary of Slang

thick n.

[SE thick]

1. [mid-19C–1940s] any drink having a dense consistency, e.g. porter, cocoa, coffee.

2. [mid-19C+] (orig./mainly juv.) a fool, an ignoramus.

3. [late 19C–1910s] a thick slice of buttered bread.

4. [1990s+] (US black) one who has a muscular, well-developed physique.

In phrases

fall in the thick (v.)

[late 19C] to become very drunk.