Using FCOM of A330-300 (Lufthansa, PW engines), assuming again 2000nm distance to destination and FL310 instead of FL370 (this quietly assumes that FL370 can be reached at current gross weight), the fuel burn difference is 3200kg.
FL370 M0.8 - 20053kg
FL350 M0.8 - 20968kg or 4.6%
FL330 M0.8 - 22034kg or 9.9%
FL310 M0.8 - 23427kg or 16.8%
One can say, roughly 4-5% more per 2000ft.