Balfour, 27, stepfather of Hudson's nephew and estranged husband of her sister, says he had a good relationship with the Hudson family.
The bodies of Hudson's mother, 57-year-old Darnell Donerson, and brother, 29-year-old Jason Hudson, were found Friday inside their home on Chicago's South Side. The body of Balfour's stepson, 7-year-old Julian King, was discovered Monday in an SUV on the city's West Side. All three had been shot.
Police say it's possible someone else drove the SUV with the boy's body inside and parked it on the West Side, but Balfour is "the only suspect in the killings (and there is) nothing to link a second individual" to them.
Balfour's mother, Michele Balfour, says Hudson's mother kicked Balfour out of the family home last year and denies her son had anything to do with the killings.
On Wednesday, police found a gun in thick shrubs in a vacant lot around the corner from where the SUV was parked.
Records show Balfour has a criminal past: He served seven years for a 1999 attempted murder and vehicular hijacking conviction.
The Illinois Department of Corrections issued a warrant for Balfour on Saturday for violating terms of his parole by possessing a weapon and failing to attend anger management counseling and a substance abuse program, according to his parole history report.
Balfour's mom insists her son is innocent of the killings.