Got some more info from Gamefaqs:
"It is NOT possible to get all 12 items in one town. 8 of them are given to you IF you go pull weeds in another town, and the other 4 are given when you pull ALL the weeds (if there are any) in your OWN town. If there are no weeds on Weeding Day, the other 3 non-mayoral characters can still get 1 of these 4 items:
Cosmos Fan
Lily Record Player
Rose Sofa
Violet Screen
So it goes like this:
No weeds ON Weeding Day:
Mayor: unlocks topiaries
Non mayor characters: item
At least 1 weed ON Weeding Day:
Mayor: pull weed(s), then get item (topiaries NOT unlocked)
Non mayor characters: item
In another town, for every 30 weeds you pull, you get an item. Keep a count yourself, as Leif may not do that for you. He only tells you how many total weeds are left in the whole town. Set cycles until done, then randomly starts to repeat:
Azalea Stool
Flower Bouquet
Hibiscus Clock
Hydrangea Bed
Lily Lamp
Pansy Table
Sunflower Stereo
Tulip Dresser
Wilted flowers and clovers count as pulled weeds, although Leif does NOT tally them in the weed count he uses when he tells you the total number of weeds left."