[dmforcier]

At a guess, I'd say that the white takes power to the switch and the paired black comes back from the switch. Thus white would be always hot and the paired black hot only when the switch is closed. This is common with a switch as you (usually) have only two choices. Bet if you pulled the switch you'd see white on one pole and black on the other.

Can you tell where the paired black is connected in the box? Bet it's to the light.

(BTW, all connections must be in a box. None of this 'wire nut splice behind the wallboard' stuff. Just FYI.)