Yeah, you could pick it up and ignore it once a week but I don't blame you for being annoyed that you have to do that because other people are lazy. Maybe it's the peacemaking response but it's kind of a lot to ask for you to pick up after your neighborhood every week because you've sent the message that it's cool with you to have your yard become a local junk yard. People around here just expect other people to overlook things when in reality if they were dealing with it it would be a bit of a bigger deal after several weekends of trash collecting.

I would just keep watching for who does it. Do you have neighbors you are friends with that may know who does it? Who may have saw something? It's something that I, personally, would address with the person doing it. It's not okay for them to trash up your property and you shouldn't have to just let it go if it's consistently going on. I would ask a neighbor I was friends with, casually without anger, and ask if they may have noticed anything.