Actually birds are known to eat hot peppers.* Usually tbey are looking for moisture when they eat any kind of peppers.
Not sure what is going on with your sweet peppers. You don't mention any symptoms of the leaves or stems, so I would rule out a virus.* I do know that too much nitrogen fertilizer will produce lots of leafy growth at the expense of flowers, but that doesn't seem to be your problem. I'm thinking the plants might have become stunted due to poor watering (over or under watering) before you purchased them.* Overwatering can cause slow and stunted growth.
The best way to get them to produce more peppers is to get them to produce more flowers.* This can be done by removing the first set of flowers that appear.* A floating row cover aka remay will keep pests away from your plants.* Bird netting also helps.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.