Translation:They write a lot on the weekends.
Much is used for uncountable nouns; a lot is for both countable and uncountable nouns. Writing feels like an edge case ("there's much writing to do" is sensible, though awkward), and should probably be technically accurate. Most native speakers would probably say "there's a lot of writing to do" as writings are generally countable, though the act of writing doesn't necessarily produce discrete objects.
Edge case, but I think it should probably squeak by as an alternative.