When you have someone “over a barrel” or put him over one you have him at your mercy, on the spot; you have him under your thumb, hook, line, and sinker.
We surmise that the literal expression was an act of mercy, arising from the use of a barrel, until better means of resuscitation were developed, in the attempt to bring a drowned person back to life.
In that method the person taken from the water was placed face down over the curving surface of a barrel, which was then gently rolled.
Needless to add, the one so placed was at the mercy of the attendant.
