We do not know that Heathcliffe is a gypsy child - there are also some theories that he could have been Irish - or a coal-miner's child, which would explain the black. At the time of the Brontes, Liverpool a huge seaport city of export, was overrun with many destitute people, perhaps awaiting an exciting passage somewhere else - one that would never materialize. Many, many of these were Irish babies and toddlers who had lost their parents through sickness or famine and had become feral. The allusion to 'speaking gibberish' in papers of the time (eg The London Illustrated News) was a reference to their natve tongue - the poor scraps spoke native Irish Gaelic. Literature is such a subjective thing, but it is in the pathos of this unjust start that I find any shred of sympathy for Heathcliffe. Whichever scenario he was born of, all were tragic. It is possible that Emily/Cathy saw this in him too and responded to it. One area where he is not a traditional tragic hero is in our identification with him at the end - there are many who fall short of seeing themselves in him - there is just something missing in the drawing of his human character?
Heathcliif was brought to the estate by Mr. Earnshaw. He was already an orphan and a gypsy child. The Roma (gypsies) are a despised people in the region where he was found. It stands to reason that he had already suffered abuse and fear at his abandonment. Mr. Earnshaw brought him home to be his second son, but the servants find him repulsive. He is set up in a sense because Hindley resents his presence in the home. Hindley's resentment becomes anger as he grows older. It is inevitable that as the oldest natural son, Hindley will inherit the estate.
Once Hindley inherits the estate, he diminishes Heathcliff's stature to a servant. Heathcliif has no money and no rights. His love for Catherine prevents him from leaving. He is not able to move nor does he have the graces of the social status that he needs in order to be able to marry Catherine. This drives a wedge between the two.
Heathcliff's love for Catherine is doomed from the start. He has no money, no true family, and he is lower class trying to marry a woman that will be expected to marry someone with money and presence. He can not support her and give her the things that Edgar can provide. Even when he has made his fortune and learned how to be presentable among the higher class, he is unable to attain Catherine’s love and devotion. He must stand by and watch her live in marriage with Edgar. Just as the reader thinks that he might actually get a chance to have Catherine she turns out to be pregnant by Edgar. Heathcliff is left to live on, devoid of Catherine’s presence but haunted by her spirit.
Heathcliff is an angry figure, but also a sad figure. He is so broken by his love for Catherine and his need for vengeance that he becomes a despondent unhappy bitter human being. His soul is condemned by his nature and actions. Yes, he is a tragic figure.