The story
From sit up + and + beg, likening the position to a dog sitting up on its hindquarters and begging by holding its front paws out.
Etymology from Wiktionary, CC BY-SA 4.0.
sit-up-and-beg
Today it means: Of a posture adopted by a person steering a vehicle (such as an aeroplane, car, or motorcycle): sitting up straight, not bent forward or leaning back. Full definition →