If a force is applied to an object on an inclined plane in the upward direction of the plain in order to balance the component of weight such that the object is in equilibrium, in what direction would the friction then act?
You can't know. Friction can go in both directions depending on if $F$ is larger or smaller than the weight component.
If $F$ is larger than the weight component, then friction must be down along the incline (in order to hold back, since gravity isn't strong enough).
If $F$ is smaller, then friction must be upwards along the incline in order to help $F$ (otherwise $F$ couldn't hold it)
If $F$ is exactly equal to, then there is no friction.
Remember that we are talking about static friction here. And static friction is a force that adjusts itself to whatever is necessary for keeping something still. Both direction and size is adjusted to fit, so it purely depends on the circumstances (on other forces).