On the '37 trucks, the weather seal is mounted to the cab, not the doors. Its not a very good seal, but it does do something. You should have some stamped sheet metal around the top and latch side of the cab held on with screws. It looks sorta like the strips in the bed only smaller. The weather strip is material covering some rubber bead material. The flat part or sewn part of the seal is held in place by the strips of steel with the bulb right at the edge. The hinge side of the door is the same stuff only held on a little different. It mounts to the door using the door panel and the front section of the window frame. Across the bottom is a rubber blade seal the rides along the door a few inches up from the bottom mounted to the cab as well.

If yours is a low cab '36 it will be the same as this.

Joe