What group wanted the Estates General to vote by head rather than by Estate?

The Third Estate, made up of about 98% of France's population, which included the bourgeoisie, peasants, and laborers.

Vote by Estate meant that each Estate was entitled to one vote per Estate, so the First and Second Estates (made up of about 2% of France's population, the aristocracy and the clergy) could vote together and successfully vote against 98% of France. Voting by head meant that the Estates would vote based on population, meaning that the Third Estate would have much more votes than the First and Second Estates.