Burney - an all conference cornerback - must sit out six games and repay roughly $575 to charity after it was ruled he received improper benefits in the amount of $1333 -- namely trips to Atlanta, Vegas and California.
According to reports, all those benefits were provided by an individual considered to be an agent by the NCAA - that person is not named, but is believed to be Chris Hawkins.
ABC11 Eyewitness News has traded messages with Hawkins on Facebook, but he hasn't responded Wednesday's rulings.
As for Williams, an all-conference safety, he must sit out for four games and repay roughly $450 out of the $1432 he received. Williams reportedly took a couple trips to California on the dime of an unnamed former UNC player.
Burney and Williams have sat out the first two games for the winless Tar Heels (0-2), which count toward their suspensions.
Both were among six underclassmen who decided to return for their senior seasons instead of entering the NFL draft.
The status of 10 other players remains in question as North Carolina prepares to travel to Rutgers. Among those players are NFL prospects Marvin Austin -- who has been suspended indefinitely for breaking team rules -- and Robert Quinn on defense, top receiver Greg Little and tailback Ryan Houston.
ABC11 contacted the NCAA directly and they said they have no other re-instatement requests from North Carolina.