In which direction does surface tension work, upwards or downwards?

It resists downward, but upwards not as much.

Surface tension has nothing to do with the gravity, or the upward/downward direction. It does not act upward or downward. The key word here is "surface". Molecules of a liquid substance are attracted to their nearest neighbors around through by a short-range interaction. The net force for a molecule inside the liquid and therefore surrounded by other liquid molecules is zero. Molecules at the liquid surface have neighbors only on one side. Therefore the surface molecules are pulled back into the liquid by a net force exerted by their fellow neighbor liquid molecules. This is where surface tension comes from.