Why does a tax create a deadweight loss?  What determines the size of this loss?

A tax makes deadweight loss by artificially increasing price above the free market level, so decreasing the equilibrium quantity.  This reduction in demand decreases consumer also producer surplus.  The size of the deadweight loss depends upon the elasticities of supply and demand.  Since the elasticity of demand increases and the elasticity of supply decreases, that is as supply becomes more inelastic, the deadweight loss becomes larger.