I can't be sure without having the car in hand, but it may be that the truck screws are loose. Unlike other brands of trucks and couplers, the Weaver coupler is a separate piece that sits between the truck and the car body. If the screw is loose, the coupler will droop. To get Weaver trucks and couplers to stay in place properly, it is imperative to use Loctite on the screw and adjust the screw tension so the truck and coupler are held firmly in place but there is no resistance to them turning. It's quite easy once you've done a couple of cars. I always check my Weaver cars when they come out of the box to make sure the truck screws are right.
It is conceivable, but highly unlikely, that you would have to put a shim between the truck and the coupler to get the coupler up to a proper height. You could make one out of plastic or metal tubing. I've got at least 50 Weaver cars and I've never had to do this, but I don't have grades on my layout so I can tolerate some variation in coupler height.