Green’s Dictionary of Slang

(W.I.) greedy; selfish.

1868		T. Russell Ety. Jam. Grammar 12: Big-eye people nubba is fe satisfy is dis wol.
1873		C.I. Rampini Letters from Jamaica 87: ‘Big-eye’ is said of anyone who is greedy or covetous.
1980		in Cassidy & LePage Dict. Jam. Eng. (1980) 41: big-eye adj. [...] greedy, selfish.