I would like to prime a part of my house now but wait a couple of weeks before painting. If I am using outdoor-rated primer, is it OK to leave those surfaces with just primer exposed to weather, likely rain?
While leaving it just in primer for the long-term isn't ideal*, I can't fathom that the primer would fail due to getting a day or two of rain. Even the pros have to wait out rain days between a primer and top coat. Heck, they may even have to pack up in a hurry during a [primer|top coat] if unexpected rain suddenly appears.
No, it's not going to be "ideal", but it won't be fatal.
* I'm pretty sure some houses are primed by their owners who then never get around to actually painting it.