I’m not 100% sure on the weekly panel stats, I just spot checked a few examples but it’s worth exploring deeper. Would help explain the monthly lumpiness for the type of analysis you’re doing.
There are been some previous resources posted in the community about normalizing patterns data over time, it’s definitely a challenge when using the data this way, with no single solution.
I’m not sure how well this correlates with Advan’s Patterns data because they do have methodology differences: SafeGraph <> Advan Methodology Differences