The first night, after eating all he could, he slept with both his pockets full and a chunk up his sleeve besides.
I wisht ye'd come out an holp me manpower a chunk up on ther choppin' block.
"thick block" of something, 1690s, probably a nasalized variant of chuck (n.1) "cut of meat;" meaning "large amount" is 1883, American English.
"to throw," 1835, American English, from chunk (n.) or by similar mutation from chuck (v.1). Related: Chunked; chunking.
To gain weight; become chunky (1990s+)
To throw; chuck (1830s+)