Jon,Morris tunes are about equally divided between 6/8s and 4/4s (or more accurately 2/2s). Both have two main beats in the bar and you dance 1-2-3-hop with the 1 & 3 on the beats.
You can even mix rhythms in the same dance. I have an LP of the Cambridge Crofters which ends with a Circassian Circle set consisting of Little Beggarman/Astley's Ride/Irish Washerwoman/Alabama Jubilee!