You can submit Progress Weigh-ins from the My Membership screen or any of your active games at any time during the week. If you have not submitted a Progress Weigh-in yet during a given week, you will see a prompt to weigh in. If you have already submitted your Progress Weigh-in for the week, you will not be able to submit another one until the following week. The deadline to submit a Progress Weigh-in each week is Wednesday at midnight PST, and the week resets on Thursdays.
Note that if you submit an initial, final, or round weigh-in for your game, it will automatically be applied as your Progress Weigh-in and enter you in that week's Progress Prize drawing.