Does Ethereal Sight let you discern reality from illusions?
No. Ethereal Sight allows you to see into the Ethereal Plane. This has no bearing on your ability to see illusions on the Material Plane. According to the DMG, the Ethereal Plane is:
A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don't hamper the movement of a creature in the Border Ethereal.
There's no mention of, for example, objects in the Material Plane also appearing in the Ethereal Plane, so you can't tell illusions from reality by their lack of an Ethereal Plane equivalent. Ethereal Sight allows you to see things on the Ethereal Plane, but that doesn't change your perception of everything on the Material Plane.