With reference to the laws of Inheritance and property ownership in the era of Wuthering Heights, how does Heathcliff inherit everything by being Cathy's father-in-law?
Although Bronte's novel was published in 1847, the narrative takes place from 1771-1803 before England's Inheritance Act of 1834 and the Wills Act of 1837. According to one researcher, C. P. Sanger, then, Emily Bronte applies earlier laws.
In Wuthering Heights, Heathcliff forces Cathy Linton to marry his son, Linton Heathcliff, so that when her father Edgar Linton dies, all his assets will go to Linton. Then, when Linton passes away, Heathcliff claims everything--Catherine's assets and Thrushcross Grange. However, he obtains Catherine's assets and property illegally.
According to the laws mentioned, when Edgar Linton's father dies, his property goes to his son Edgar for life, then to Edgar's sons "in tail" (the male order). Since Edgar has no son, the property passes to Isabella, who holds a life interest with the remainder to her sons in tail. Thus, after Isabella's death, Linton Heathcliff becomes tenant in tail.
However, this order is not followed. Ellen Dean importantly narrates that Heathcliff kept Thrushcross Grange in his wife's right and also his son's:
"I suppose, legally at any rate, Catherine destitute of cash and friends, cannot disturb his possession."
The researcher mentioned above states that even if Isabella had had an estate tail (male claims) or an estate fee-simple (total ownership), as her husband Heathcliff would have no right to her estate for life because Isabella was never in full possession of Thrushcross Grange.
Significantly, Ellen Dean is aware that Linton Heathcliff cannot dispose of his property by will to Heathcliff because he is a minor. But, what happens is that Edgar Linton dies before he can enact a plan to prevent Heathcliff from taking his property. So, his money passes to Catherine and then to her husband, Linton. Although he is a minor, before 1838 and the Inheritance and Will Acts, he can make a "will of personalty"; so, Heathcliff forces him to make such a will, leaving everything to his father.
Clearly, Heathcliff is wrongfully in possession of Thrushcross Grange, but Catherine is too destitute to contest his ownership. As the holder of Hindley Earnshaw's mortage of Wuthering Heights, he also owns this, and he has his personal wealth acquired mysteriously, so he can fight Catherine if she tries to claim her father's estate that has passed to her husband Linton, who then willed it to Heathcliff.