I vote no weeds...
Myself and a few other people actually host weeding events in the train station forum.
Mine are when Leif wants to do the weeding mini game... to pull weeds like weeding day and when they are all pulled, he will give you a weeding day item. And it can have as many as will fit in your town, 4, doing it and everyone who at least pulled 1 ((or so they say but I say 5 to be safe)) gets an item.
So, it's possible to get the items in other ways other than weeding day. =3