Wight began competing in hillclimbs at an early age, but in September 1992, still only 21, he was badly injured in a road accident when the brakes failed on his Hillman Imp. It was feared that he might be paralysed, and he remained in hospital for more than two months, but by 1993 he was not only out of hospital, but competing in - and winning his class in - hillclimbs once again.
In 1995, Graeme married. Two years later, after a time in a Vision sports car, Wight won the Scottish Hillclimb Championship outright driving a Pilbeam. 1998 saw his first year of competition in the British Championship, at first in the two-litre class but then in the unlimited-capacity division. In 2000, now driving a Gould, he broke the hill record at Doune by 1.49 seconds, an astonishing margin in hillclimbing and indeed the biggest improvement in an outright record in BHCC history. After finishing fourth in the Championship that year, he finally reached the top in 2001 and 2002, winning the title in both years. Graeme became the first driver to complete the course at Shelsley Walsh in under 25 seconds when he recorded a time of 24.85 seconds on Sunday 2 June 2002, in the presence of Sir Stirling Moss. In that same year, he became the first reigning British Hill Climb Champion to be invited to drive at the Goodwood Festival of Speed.
He was runner-up to Adam Fleetwood in 2003, but after that things started to go wrong for Graeme. He was Fleetwood's main rival in the first part of the 2004 season, but delays in the appearance of his new car meant that he barely competed after mid-June and could manage only eighth place in the championship. Continued development problems in 2005 meant that he was never in the running in that season's championship and only rarely qualified for the run-offs. He was also absent from the 2006 championship, but still hopes to return to competition.
This new car, christened the "GWR Predator" and of an entirely new bespoke design, is the product of a huge amount of effort. The concept of the car was to employ an ex-Arrows F1 Cosworth V10 as the powerplant, using the engine's inherent light-weight and power to allow even further increases of power to weight ratio. In October 2006, however, Wight announced that the V10 engine was to be sold as he had grown frustrated of being unable to compete due to continual engine problems. He decided instead to power the car with the Ex-DTM 2.6 V6 Opel Cosworth, previously used in his Gould GR51, though in the event the V10 was used in 2007 after all.
The Predator represents a huge leap the level of technology employed at what is ostensibly an amateur sport, with its combination of its ultra light weight, innovation and all-round complexity. Wight had a frustrating 2007, but late in 2008 the Predator finally came on song, and at the final round of the season, at Doune, he won the first run-off and came second in the other. Wight was thrilled with his victory, saying that "the car has never been that good before" and that it had been "amazing" through the Esses.
His father, also Graeme Wight and sometimes known as Graeme Wight, Sr. to distinguish him from his son, also competed in hillclimbs, often sharing a car with his son.