Weekly promotion or bonuses is what I like and what's on my mind is something like a rake back or free bet depending on how much you wager on that week and of course you should have a wagering requirement as many user would probably take advantage on that kind of bonus considering that it is a weekly bonus.
But usually, to get a weekly bonus, a level requirement or a percentage of your account is required, which will be calculated by how many bonuses you can get. If you are a small gambler who never or rarely bets big money, you will likely not meet the weekly bonus requirements. But it also depends on the policies of each casino towards its members. But you can still get promotions from programs offered by casinos, so you can take part in every promotion at the casino, of course, with the terms and conditions that apply.
Depends on the requirements and your activities inside the house. If you don't meet that said requirement, then expect that you might not get anything. It's an additional perk that accompany by wagering or activities that you are doing inside the house.