Can a crop’s task repeat, like weekly weeding until harvest?

Yes, and you set it once for the crop, so nobody has to remember the next pass. In Charts > Tasks, open the crop, click Edit and set the task’s Recurrence: Repeat every 7 days, Until ready to harvest for weeding (other end points: Until transplanted or direct seeded, Until harvested).

Every new planting of the crop then gets its repeated tasks on the right dates, and they move with the planting. Recurrence is for the crop’s own tasks, such as weeding or trellising; the sowing and transplanting steps happen once.

For plantings already in your plan, the Plantings button sends the new task list to them; it replaces tasks you changed by hand on those plantings.

The steps are in How plantings create your tasks.