Whatever the origin, John Willes realised that the pace and bounce generated by this raised arm action made the delivery potentially more difficult to play than a conventional underarm one and so he adopted the style himself with his arm coming through at shoulder height.
The matter was controversial enough for a law to be introduced in 1816 into the Laws of Cricket to prohibit roundarm: The ball must be bowled (not thrown or jerked), and be delivered underhand, with the hand below the elbow.