Using finite size scaling we relate the fall of the transition temperature with reduced thickness to the temperature dependence of the bulk superfluid density and the amplitude of the perpendicular phase correlation length. The scaling predictions agree quantitatively with Monte Carlo estimates of the Ary-model and experiments on 4He films. We also investigate the behavior of the helicity modulus for different system thickness, showing the crossover from the universal Kosterlitz-Thouless jump to the three-dimensional behavior. © 1992, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.