Yes, weed killer does kill moss on your patio. The only reason people think it won't is that either 1) they don't use weed killer on their patio or 2) they do use weed killer but don't see immediate results. The thing about moss spores is that they are always in the air. If you apply weed killer correctly then it will kill off your moss over time, but this may not happen overnight - you'll need to be patient!