First off, having now seen Bill Belichick in a suit, I understand why he wears hoodies now. The suit is not a good look for him — in a hoodie, he looks like a Dark Lord. In a suit, he looks like a menacing Pillsbury Doughboy.
That said, I kind of appreciate that Letterman really does go after him on DeflateGate. It’s playful needling, but it’s enough needling to clearly make Belichick uncomfortable (or maybe it’s just the suit that makes him uncomfortable).