Your average gets reset whenever you change a tier. I think its been very rare for somebody to advance a tier and be able to keep their average where it was. There is a rounds played and average requirement necessary to advance in tiers. Anything other than stroke play (i.e. match play, alternate shot, CTTH/blitz) has no effect on your average, but will still get you experience points towards advancing your level. So the leader of the tourney could very well only play stroke rounds on the weekly tournament, and be honing his/her skills in match or AS games to be able to score low in the tournaments.
Also, whatever tier you enter a weekly tournament in is what you will stay in for that week, even if you advance a tier during the week.