I've looked at several info pieces on "chicken crime scene" analysis, and yours doesn't seem to fit any of them exactly. Supposedly, weasels will kill several birds, not just one. An aerial predator is the closest fit, but none of the things I've found address cats either, so I wouldn't rule that out.
I would get a trap and see what you catch. Bait it with a very small amount of canned cat food. I got a set of two traps at Tractor Supply, one is possum/coon size, and the other would catch a weasel. We've caught as many as 3 possums, on 3 consecutive nights.
A simple A-frame chicken tractor might be your best bet for daytime use, while you're not at home. It's always upsetting to lose one - I understand completely.