Surrounding your crops with fences is probably your best bet. But also yes, clearing any weeds you find before they spread is a good idea. If fences are too inconvenient, paths may help somewhat. Weeds can destroy them, but at least you get a warning before anything valuable is damaged that way.
If you cover every free tillable spot with path, they will not spawn. Until you accomplish that, always visit on Mondays to get rid of the weeds before they spread.
Paths will not stop them from spreading, but I think they will only spawn on free tiles.
Until you can afford the golden clock (which will be a very long time for most) they will keep forming. Hardwood fencing s your best bet, cause, yes, without the stupid clock, fences decay on Ginger Island too.
If you keep your farm on Ginger small enough thus having generous untilled space, and check early in the week, it seems the spawns don't immediately spread to Crops and I haven't had problems for a couple seasons now. But the more industrious out there (ie: everyone) do like to max out the Ginger Farm and using Pathing does well to reduce or eliminate Weeds. The caveat being that growing Trees outside requires a season of growth with nothing next to the Tree base so you'll need to be more vigilant until they're fruiting.