Three ideas:

1) No one can enter a week mid-week. They have to be site members at the start of a round to be in the round. This may help with the groups of not-very-actives which start showing up in the middle of the week.

Next: It’s a huge advantage to be able to play right before the game’s supposed to end. So:

2) Create groups based on users’ time zones, so everyone competing against each other is active at roughly the same time, and/or…

3) Switch around the time, and possibly even the day, from round to round, to shake the advantage up. I can tell you, for example, that moving the time back 2 hours would give me a huge advantage, while pushing it forward 2 would put me at a large disadvantage.