In the novel, Mr. Earnshaw finds the homeless boy Heathcliff described as a "dark-skinned gypsy in aspect", living on the streets of London and takes him in and eventually adopts him. I seem to recall other mentions in the novel of his dark complexion and dark or "black" eyes.
There was a film version in 1992 with Ralph Fiennes and Juliette Binoche as Heathcliff and Cathy that was pretty well done and includes the second generation story of the children of Cathy, Hindley and Heathcliff which wasn’t in the Laurence Olivier and Merle Oberon version.
Interestingly Merle Oberon was herself part Sri Lankan and Māori, born out of wedlock in Bombay to a 12-year old girl and raised by her grandmother, who also was only 14 when she gave birth to her daughter, growing up thinking her mother was her older sister, something that Oberon kept a closely guarded secret.
Healthcliff simply wasn’t a mulatto despite his gypsy eyes - any more than Alexander Hamilton was. Yes, Merle Oberon seemed to be of mixed blood but that doesn’t make Heathcliff anything other than British. The Welsh often have very dark eyes as do the “black” Irish (of which my father and myself are descended from).
Interesting stuff about Oberon; some of which I knew, some of which I didn't.