The weeds you are seeing are likely from the feed the birds have been eating and passing through their systems (chicken Manure) Many bird feeds are a combination of different plant and grain seeds. You don't want to use weed killer since that will harm or kill the plants.
So, as far as they are concerned, you can pull them out as they grow. Or add a layer of mulch on top, which will keep weeds from further developing.
Now to determine is the soil is too acidic, purchase a pH meter or soil test kit at a home improvement center. They are around $10-15 dollars. Lime is often used to balance acidic soils.
To save your vegetables without moving them, you can use lime to balance pH, add fresh topsoil, or try to leach out the soil by running water through it.
