Around three or two weeds will grow every new in-game day (which starts at 6 a.m.) as long as your ordinance isn't Beautiful Town. If you just changed it, wait a day or so, and you should start seeing those weeds. You can also time travel days ahead to grow them faster.
I don't think that you can just change the date as far as you can and get a ton of weeds. There's specific ways to do so. I think that the most you can time travel at a time to get weeds is maybe month by month or year by year, but I'm not positive on this since I don't time travel. Maybe someone else can comment if they're more familiar with time traveling for weeds.