Under the influence

I am wondering why we say that someone is "under hypnosis?"

I don’t think it is negative, but is it accurate? You are not under anything. Most expressions utilizing "under" imply loss of control, or something shady or illegal, like:
Under a spell, under investigation, undercover, under the table, under anesthesia, under the weather.
Maybe it's more accurate to say "in hypnosis," "in trance," or "in a hypnotic state."

Who wants to be under anything? Except a soft blanket of relaxation, which is how many people feel while experiencing a hypnotic trance.

Under is a weird word. Look at it for a while and you might begin to wonder if it is a word. It comes from Old English, but I would venture a guess that there is a similar word in German.