Like many Australian shooters I have shot kangaroos and pigs in the thousands and I suppose these would be similar in size to your deer.
Large quick expanding bullets are the most destructive and lethal.
In terms of velocity, if you think about it, a 400 grain Speer from a 458 will have much higher velocity as it travels thrugh the animal than say a 243.
I think Weatherby was right in an way, but it is velocity through the animal not velocity at impact.
Also, it seems to me that momentum from both observation and theory is a large contributor. Bullet momentum will cause more flesh to move or the same flesk to move out of the way quicker.