I've created apps that read and write data to entities I created in CDS. The users of my apps however complain that the reading and writing of the data (typically through PATCH or FILTER functions) takes longer over weekends than during the week. I have not experienced this myself, but this has now been going on for a number of weeks, and every week I get complaints of performance issues over weekends. Are there reasons why this might happen?
There isn't any known issue with performance over the weekend. If anything, you should see superior performance as these are not usually peak hours. This should mean that this isn't a resource availability issue, although always possible.
This does depend on how busy your weekends are, though. It's still possible to overload an individual environment's CDS instance with too many requests. On the backend, these requests generate an async job that runs when it can. If you are making a substantial number of requests, you're going to generate more of these async jobs and create a backlog. Once you get a backlog, everything tends to slow down until the jobs are cleared out. This happens both in the cloud and on-premises.
On that note, if there is something on-premises about your configuration (maybe you run some data through a gateway to another data source?) you'll want to look into that configuration first. By and large, the cloud should remain consistent so the breakpoint is often with the on-premises part of a given solution.
It's possible that your app has some fine tuning you can apply to it. This shouldn't really affect any Read/Write actions against CDS but your expressions, the functions you're using, etc. can be a factor in how the app performs.
This brings up another good point: Are we talking about a model-driven app (Dynamics) or a canvas app (PowerApps)? You create either one from the Maker Portal but model-driven apps are probably better addressed on the Dynamics forums as they run on separate functionality. We mostly handle canvas apps in this space.
Licensing can be a factor in performance, do you know what your weekend users have assigned to them? If they're using trial/Standard licenses, they will always perform a little slower than if they have a standalone/Premium license assigned. We also have API limits and other thresholds in place that can be hit, similar to the async job issue I mentioned above.
If you go through all of this and it's still not clear, you can always set up a support incident through the Power Platform Admin Center. We'll need reliable reproduction in order to further the issue but we can take a look.