Surface Tension

This is due to atmospheric pressure and gravity?

I mean, intermolecular forces, yes, but is the extent to which it rises due to surface tension?

Also checkout Capillary Action.
It is also known as Surface Energy.

Notes

It is the tendency of liquid surfaces at rest to shrink to the minimum surface area possible.

At liquid-air interfaces, this is due to the greater intermolecular forces of attraction of liquid molecules (adhesion) to the liquid molecules compared to that of the air molecules (cohesion).

There is an inward force and an outward force tangential to the surface. This outward force is referred to as the surface tension.

This is similar to liquid being covered in an elastic membrane, but in elastic membranes, the tension is due to the amount of deformation, while surface tension is an inherent property of the liquid-vapour or liquid-air interfaces.

Its dimensions are force per unit length or energy per unit area. Because of this, it is also called surface energy. The term surface energy is more common when used with solids.