If I go away for a weekend, what can I leave behind to test if there is any kind of activity in my home while I'm away?

Nothing, there is no test, even if it is, paranormal works various ways

But if leave, motion detector cameras, heat sensors, movie or security cameras

If there was a fool proof test... it would be used all the time, by everyone. But the spirit world does not work like that.

If you have something that consistently happens in your home... set up something around that.