When you say it opens at the top what do you mean? The weir door should pivot on some posts on the bottom of the door. The pull of the pump pulls the stuff into the skimmer and and pulls the door down as it comes in. Then the door goes back up to keep the stuff from leaving the skimmer area.
They are called weir "doors" but they work like a door on its side.. Hinged at the bottom and opens and closes at the top.. When the pump is running the door should have a small amount of water flowing over the top of the door.
Water level is also important.. The higher the water, the less skimming action.. But, you don't want the water to drop below the skimmer's mouth, so the best compromise is right at the middle of the skimmer or slightly lower.
If you think you have an odd skimmer, post a pic or two, so we can both be on the same page.