It looks like Belichick is in the clear and had no idea what was going on. When the media reports came out, he asked Brady directly if he had any knowledge of this and here is what Brady said per the Wells Report.
On Thursday, January 22, Belichick reportedly discussed these issues for the first time with Brady, shortly before a team meeting. Belichick asked Brady directly whether he had any knowledge about any of the issues raised by the press since the AFC Championship Game.
According to Belichick, Brady said “absolutely not.” Belichick stated that he then asked if Brady or anyone Brady knew had tampered with or in any way altered the footballs. Brady again denied any knowledge or involvement. Belichick recalled that Brady also explained that once he 100 inspects and approves game balls, those balls are exactly as he likes them and that he would not want anyone to do anything to them after that point.
Belichick believed Brady. Belichick and Brady attended the team meeting, and Belichick told the team that there was “not one shred of truth” to the deflation allegations. When given the floor, Brady repeated what he had told Belichick about wanting game balls to be exactly as he approved them.
If you believe the Wells Report, Brady told Belichick an outright lie.