it appears that once a year on a certain date (differs in different regions) Leif gets ticked off with all the weeds in people' s towns so he meets them at the plaza and tells them to start weeding and he will give a special piece furniture if they collect 30 or more, the gifts he gives are all pieces of furniture themed on flowers. You can also visit friends towns and collect weeds there. if by chance you have no weeds in your town, you get topiary ( 3 different ones) passed to Isabelle to add to your forthcoming projects list.
This also happens if you time travel for say a month.
Leif will be sleeping near your house and will ask you to help him weed and he'll reward you on how great you do.
(Like, if it's 60 weeds you have, 40-ish will get you a Perfect fruit and getting them all will get you a special piece of furniture made by him)
Such as a Rose Sofa, Violet Screen and Lily Record Player (Which are the three I currently have)
If those are the type of furniture you're after, that is.