I've subscribed to the weekly newsletters of several Stack Exchange sites, mostly smaller ones that I'm interesting in but don't regularly visit. I just received all of them in my inbox at once.
I would prefer it if the newsletters for different sites were sent at different points during the week. It could give me something to read every day; with the current setup I'll probably skip a few of them.
Since (I assume) large sites are more likely to have subscribers, it might make sense to mainly ensure that they are spread out during the week, with the smaller sites distributed more randomly.
Alternately, schedules could be user-specific; either spread out during the week automatically or manually configured. This would require a different newsletter be generated each day, using a rolling one-week window, but this doesn't seem like it would be a prohibitively expensive operation.