The usual attempt to explain surface tension shows two molecules in a surface and in the bulk, where the surface molecule only experiences attractive forces from one side, while the bulk molecule experiences attractive forces from all sides. This image is misleading because it makes us believe that the understanding of static forces was sufficient to understand what is really happening on the molecular level.
Actually, the Lennard-Jones-Potential is a good model for understanding the balance between short-ranged repulsive and long-ranged attractive intermolecular forces, but it implies that, statically, the molecules would be in equilibrium as soon as they get into contact with each other at the equilibrium distance, just like sticky spheres. From that point of view, there would be no inclination to believe that the molecules in the surface have a greater or smaller distance from each other, than the molecules in the bulk, just because that distance is (supposedly) equal to the corresponding unchanged distance value $r_m$ of the Lennard-Jones-Potential.
However, the static picture is not the whole story. Otherwise, what would be the difference between a liquid and a solid? They both are characterized by molecules getting in more or less tight contact with each other due to attractive forces. But in the liquid, the kinetic energy of the molecules is enough to make them constantly swap their places, as opposed to the solid, where molecules largely stay in their determined lattice sites. So, undoubtedly, molecular motion is essential for understanding the liquid state.
As soon as motion of the molecules comes into play, it is rather easy to understand what its effect on the relative distance between molecules will be. If you just consider two molecules with a Lennard-Jones potential, they will somehow oscillate in this potential. But contrary to a movement in a purely harmonic (or at least a symmetric) potential, whose average position is strictly in the center where the potential also has its static minimum, the Lennard-Jones potential is "extremely" asymmetric, resulting in the fact that any motion will shift the average position away from the static equilibrium to greater distances, where only the weaker attractive forces have to be surmounted. This is shown in the following graph (note, that the "average distances" are only roughly depicted in the center of the horizontal bars, while the asymmetry of the motion itself would also shift the average yet a little more to the right)
In the bulk liquid, molecules experience collisions with other molecules from all sides, which limit their motion, and hence, also limit the Lennard-Jonesy increase of their relative distance to each other. But at the surface, the repulsive collision part of the forces is missing on one side, and so, the molecules there are only kept to the liquid due to attractive forces. The corresponding greater liberty of motion leads to an increase of average intermolecular distance at the surface. Since all this depends on collisions (or lack thereof), i.e. a dynamic (mass-dependent) effect, this once more underlines that any static picture of the liquid state is insufficient.
What remains to be clarified is the relation between this picture and surface tension. For an answer, compare a planar region of the surface with a positively curved region of the surface. A molecule located at the curved surface region will clearly have less neighbours than its cousin located at the plane surface region, just because of the curved geometry. But there are also two kinds of neighborhood: the neighborhood for the short-ranged repulsive forces is narrower ("sharper"), while the neighborhood for the long-ranged attractive forces is wider ("more blurry"). The consequence of this is that, as curvature increases, the number of repulsive neighbors decreases faster than the number of attractive neighbors. Therefore, for curved surface regions, the attractive forces will dominate, and hence, the molecules there will tend to get drawn into the bulk, even though the local surface region still shows lower density (but a little less so than for the plane surface). The bottom line is that there is no contradiction between lower surface density and curved regions getting pulled into the bulk. You don't need to invent a pre-tensioned membrane concept to explain surface tension.
Consider the analogy, that you are dancing pogo in a crowd at a punk-rock concert. Your desire to be part of the group is the analogy to the attractive forces between molecules, which keeps the group together, although there are always collisions which keep you and your fellow dancers apart. If you are inside the bulk of dancers, you will not notice any anisotropy that would draw your motion preference into one or the other direction. But if you are at the boundary of the dancing group, you are competing with the other dancers at the boundary for a place inside (wouldn't punks actually defy the laws of capitalist competition, what an irony...), which, by the way, also constitutes a kind of surface tension because it favors a spherical boundary of the dancing group. And albeit attraction keeps the group together, there is still the effect that the density at the boundary is a little lower, because you are always bumped at from inside the crowd.