If the beefsteak tomatoes aren't touched even when they're ripe, it sounds like a creature called 'a neighbor'.* Another possibility would be birds taking the tomatoes away.* They eat them for the moisture, so if it's birds you can stop them with setting up a birdbath and use bird netting to cover the plants. * If you are certain that's not it, I would suggest you sprinkle some household flour around the site so you can id your pest.* Sprinkle the flour at night and check for the footprints in the morning.* Then you'll know how to proceed.* I suspect if it's one of the small animals you mentioned, an electric fence would do the trick.* You'll need to know which one so you know how to structure the fence.* Here's a guide for the footprints.
Once you know who it is, we can go from there.
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.