Fixing letterbox that flaps in the wind

Like most new houses these days, our letterbox is on the wall outside our house, as opposed to being in the door.

Unfortunately, when it's windy the flap blows about in the wind. This is incredibly noisy at night, but it also means that water gets into the letterbox, which then doesn't dry out properly, and so post gets wet when put in by the postman.

The flap lifts outwards, not inward, so you pull on it to open it.

The flap has no tension in it, there's no spring or anything to hold it down. The flap spans the entire width of the postbox, then directly below the flap is they keyhole, which opens the lower-half of the letterbox so you can retrieve post.

The flap can't be removed from the letterbox (I was initially considering sticking some rubber washers on the hinge at each side to make it really tight).

I was thinking maybe to attach (glue?) some weights along the flap on the inside to make it heavier. Or another alternative using magnets of some sort, but then there would be problems getting it to close flush as there's not much of an overlap from the flap to the front of the letterbox?

Anyone have any suggestions?