I don't recall any specific explanations in the books, though there may be.
The line of thinking behind that seems to be that large weapons can only do so much damage to medium/small creatures because there's only so much medium/small creature tissue to be damaged at one time--can't hurt what's not there. Large critters have more tissue to damage, so more of the energy from the weapons gets translated to damage.
If you drive a nail into a 1/4" board, only the quarter inch gets damaged, despite the nail being 2" long. If you drive that nail into a 4" board, a whole 2" of board gets damaged by the nail. Make sense?