Only Associations who have at least 4 members when the Tournaments are scheduled will take part on that week's Tournament. Matches are played Saturday and Sunday every week, except for the last week of the Season, in which case they're played Friday and Saturday to avoid conflicting with the Season update.
Associations who have 6 members will play vs other Associations with 6 members. Associations with 5 will play with others who have 5, and same for Associations with 4.