Cutting weeds is part of it, which is what I was referring to. And yes, it is only a part.
Yes of course it is. As is painting over graffiti, picking up litter, towing abandoned cars, etc.
The more important part, though, is enforcing minor laws. Which can include littering, keeping your property maintained, etc.
The purpose of crime control is to effect behavior. Whether that means keeping your city clean, maintained, or crime free.