Solved! I discussed this with a co-worker and he found that my Google Ads feature was turned on. I understand this is used by Google to push ads or see what sort of things I've been doing. Apparently, then, this features turns on WiFi to transfer information...I guess it wants to use WiFi (if available) to transfer so that it doesn't detract from my data plan.
I can't find that particular setting now...he did things so fast, I couldn't keep up with it. But my WiFi stayed off all night long...the first time in several months.
Kurt