In addition to my own research, I found an interesting essay discussing some of the semi-autobiographical parts of Aurora Leigh, and how Barrett Browning's character was consciously and unconsciously influenced by her own life. I've referenced that in some places; other parts are from my own outside reading.
Aurora's mother died when Aurora was four, leaving her without a maternal figure in her life. The consequences were extremely important, yet the character's memories of her mother are different from Barrett Browning's memories. For instance, Aurora remembers her mother visually most through a posthumous painting of her, which brought to mind
Ghost, fiend, and angel, fairy, witch, and sprite,
A dauntless Muse who eyes a dreadful Fate,
A loving Psyche who loses sight of Love,
A still Medusa with mild milky brows
All curdled and all clothed upon with snakes
At the same time, her memories explicitly contradict this, and Aurora knows that this was not her mother. She then writes that the woman could have been all those things,
Or my own mother, leaving her last smile
In her last kiss upon the baby-mouth
Barrett Browning wrote a passage in a letter shortly after her mother's death which is quite reminiscent of her later writing in Aurora Leigh (from Leighton's Elizabeth Barrett Browning, page 55):
Her voice is still sounding in my ears - her image is in my heart - and they are to be loved, however unreal they may be!
We see some similar parallels with Aurora's father, especially given that she has a close relationship with him - until his death, nine years later - which mirrors Barrett Browning's relationship with her father, until she eloped with Robert Browning, which cut off their correspondence. Aurora's father attempted to impart a love of learning to her, from an early age:
He sent the schools to school, demonstrating
A fool will pass for such through one mistake,
While a philosopher will pass for such,
Through said mistakes being ventured in the gross
Barrett Browning exhibited the same devotion to her father, even though he has been variously described as "despotic" and "overprotective and tyrannical". All the same, he (as well as her mother) encouraged Barrett Browning's reading, education, and subsequent writing. Indeed, we see many connections between this real-life education and Aurora's books. Names run off like a stream of rushing water: Theophrast, Aelian, and other Classical writers (who are referenced again in allusions later in the poem). There is no doubt that the relationship with Barrett Browning's father echoes in the writing in Aurora Leigh.
As the essay I cited earlier points out, Aurora's interactions with Romney Leigh can also be viewed as commentary on her own life. We see clear disconnect between the two from the beginning, as they go through adolescence and young adulthood together:
We came so close, we saw our differences
Too intimately. Always Romney Leigh
Was looking for the worms, I for the gods.
A godlike nature his; the gods look down,
Incurious of themselves; and certainly
'Tis well I should remember, how, those days
I was a worm too, and he looked on me.
Aurora has her eyes set things completely different. Her goals in life, her aspirations, rest on poetry, the way she can look "for the gods" and a better understanding of the world. Romney has different designs, and different beliefs as to what a female poet can and cannot do.
The essay points to an early relationship between Barrett Browning and Hugh Stuart Boyd. There was clearly a disconnect between the two:
In her diary accounts of the relationship, she describes her unrequited affections. According to Laurelyn Douglas, "For a year her entries calculate the bitter difference between his regard and her own, and she wonders if she can ever hope for reciprocation" (Douglas).
This seems somewhat ironic, insofar as Aurora is the one to reject Romney's advances, whereas Boyd appears to have inadvertently rejected Barrett Browning's advances. It begs the question of whether this reversal is a reflection on that courtship, and whether Barrett Browning agrees or disagrees with how it ended.