My math isn’t good enough to figure out the weeks quite yet, but this will give you the months with no problem.
You might be able to alter this to get you the weeks. I would say you need to figure out how many degrees you need the hand to move for each week. On the above the months have to have the hand move 30 degrees each month, just like the hour hand moves only in reverse. That’s the (-( part of above. The +15) aligns the hand to the center of the month name.
UPDATE: I played with my expression and figured out that this will match the weeks of the year in your example picture.