Hey there Notahappycustmr,
Thanks for your post!
If you're seeing power being used habitually very late at night or very early in the morning, then its very likely that the appliance responsible is your hot water system. If you have a storage hot water system (which looks like a large tank), then this essentially operates in a similar way to a kettle. The water will heat up overnight at the same time to ensure that hot water is readily available to you throughout the day.