Why does significant condensation gather on my bedroom windows overnight?
I would guess that the problem is not a draft from the windows, but moisture in the room, probably caused by having two people sleeping in a closed room.

The warm, moist air in the room will hit the cold window and water will condense.  To eliminate the problem, get more air circulation - open the door, or open the window a tiny bit.  At least try it for a couple of nights to see if that solve the problem.