Balfour is charged with murdering Hudson's mother Darnell Donerson, brother Jason Hudson and 7-year-old nephew Julian King in the Englewood neighborhood in 2008.
The jury, which is made up of six men and six women, began deliberating the case just before 5 p.m. after receiving instructions. The panel deliberated late into the night, dining on chicken, ham, and turkey sandwiches.
By early Wednesday evening, jurors had already sent a note to the judge asking if they could receive trial transcripts. It also asked if keys found on William Balfour at the time of his arrest included one for the Hudson home, where Hudson's mother and brother were killed.
Jurors finished up for the night around 9:30 p.m. They are being sequestered at an undisclosed location and will resume deliberations Thursday morning at 9:30 a.m.
Earlier, Jennifer Hudson shielded her eyes and wept as prosecutor Jennifer Gagby showed graphic autopsy photos of the singer's murdered relatives in her closing argument.
Bagby said Balfour "left that innocent child to die in his own pool of blood," referring to the 7-year-old King.
Of Donerson, Bagby said Balfour "fired that gun over and over and over at her."
But in her closing, defense attorney Amy Thompson said there was no credible physical evidence linking her client to the murders.
"There is DNA on this gun," Thompson said of the alleged murder weapon, "just not William Balfour's."
The case against Balfour, Thompson said, was the result of a rush to judgment by investigators influenced by Jennifer Hudson's celebrity. Balfour, she said, was "a pre-chosen defendant."
Prosecutor James Mckay, however, said Balfour would have to be "the unluckiest man in the world" to be wrongly-accused of killing his estranged wife's family, citing "a tsunami of evidence."
Several witnesses, the prosecution said, saw Balfour with the gun in the weeks before the killings. Many of them testified that he spoke of harming the Hudson family dozens of times.
The prosecution also said cellphone data placed Balfour near the Hudson home crime scene on the morning of the killings.
Of his multiple girlfriends, one of whom testified Balfour confessed to her about the killings, Thompson acknowledged her client was "a dog."
Prosecutor McKay countered by saying, "calling the defendant a dog is an insult to dogs."